1. Algebra 1 Predicting Patterns & Examining Experiments Unit 7: You Should Probably Change Section 2: Making Arrangements

2. Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. How many outfits?

3. Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? How many outfits?

4. Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? How many outfits? Tyrone navy/green watermelon orange/red lime/orange green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo

5. Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? How many outfits? Tyrone navy/green watermelon orange/red lime/orange green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo There are four pairs of shorts can be worn with each of the three shirts. So, there are twelve different outfits. There are four pairs of shorts can be worn with each of the three shirts. So, there are twelve different outfits.

6. Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? Tyrone needs to update his wardrobe, it’s been a few years and he’s tired of hiding behind palm trees. He has bought four pair of bermuda shorts and three t-shirts. How many different outfits can he make? How many outfits? Tyrone navy/green watermelon orange/red lime/orange green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo green camo gray camo brown camo There are four pairs of shorts can be worn with each of the three shirts. So, there are twelve different outfits. We could have just said: 4 3 =12. There are four pairs of shorts can be worn with each of the three shirts. So, there are twelve different outfits. We could have just said: 4 3 =12.

7. Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) How many KS plates?

8. Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) How many KS plates? License plate example: BCZ 503 License plate example: BCZ 503 A B C... Z A B C... Z A B C... Z 01234567890123456789 01234567890123456789 01234567890123456789

9. Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) How many KS plates? License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits

10. Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) How many KS plates? License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits The total number of license plates are 262626101010 = License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits The total number of license plates are 262626101010 =

11. Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) Kansas license plates contain three letters followed by three numbers. How many unique license plates can be in each KS county? (assuming all 26 letters and 10 digits are used) How many KS plates? License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits The total number of license plates are 262626101010 = 17,576,000 per county. License plate example: BCZ 503 26 letters, 26 letters, 26 letters, 10 digits, 10 digits, and 10 digits The total number of license plates are 262626101010 = 17,576,000 per county.

12. In how many ways can you arrange 7 books on a shelf? Book Arrangements

13. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement Book Arrangements

14. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements Book Arrangements

15. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements (notice we put a B after and before the previous arrangement) In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements (notice we put a B after and before the previous arrangement) Book Arrangements

16. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements Book Arrangements

17. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements (notice we put a C after, in the middle, and before the previous arrangements) In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements (notice we put a C after, in the middle, and before the previous arrangements) Book Arrangements

18. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Book Arrangements

19. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Book Arrangements

20. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. (notice we put D’s all throughout the previous arrangements) In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. (notice we put D’s all throughout the previous arrangements) Book Arrangements

21. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements

22. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements booksarrangements 11 22 36 424

23. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements booksarrangements 11 22 36 424 there are 5 locations for book E

24. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements booksarrangements 11 22 36 424 there are 5 locations for book E for each of the 24 arrangements

25. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements booksarrangements 11 22 36 424 5524 there are 5 locations for book E for each of the 24 arrangements

26. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. What is the pattern? Book Arrangements booksarrangements 11 22 36 424 5120 there are 5 locations for book E for each of the 24 arrangements

27. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11 22 36 424 5120

28. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11 212 = 2 36 424 5120

29. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11 212 = 2 3123 = 6 424 5120

30. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11 212 = 2 3123 = 6 41234=24 5120

31. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11 212 = 2 3123 = 6 41234=24 5 12345 =120

32. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Book Arrangements booksarrangements 11 212 = 2 3123 = 6 41234=24 5 12345 =120 There are n! ways to arrange n items.

33. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Book Arrangements booksarrangements 11 212 = 2 3123 = 6 41234=24 5 12345 =120 There are n! ways to arrange n items. n! means to multiply n by all the numbers from n on down to 1.

34. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. Notice the pattern? Book Arrangements booksarrangements 11! = 1 22! = 2 33! = 3 44! = 24 55! = 120 66! = 720 77! = 5040

35. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. There are 5040 ways to arrange 7 books on a shelf. In how many ways can you arrange 7 books on a shelf? I will call the books A, B, C, D, E, F, and G. Arrangements: 1 book: A : 1 arrangement 2 books: AB BA : 2 arrangements 3 books: ABC ACB CAB BAC BCA CBA : 6 arrangements 4 books: ABCD ACBD CABD BACD BCAD CBAD ABDC ACDB CADB BADC BCDA CBDA ADBC ADCB CDAB BDAC BDCA CDBA DABC DACB DCAB DBAC DBCA DCBA : 24 arngts. There are 5040 ways to arrange 7 books on a shelf. Book Arrangements booksarrangements 11! = 1 22! = 2 33! = 3 44! = 24 55! = 120 66! = 720 77! = 5040

36. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists?

37. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists? There are 11 songs, but only 4 will be arranged.

38. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists? There are 11 songs, but only 4 will be arranged. SOLUTION #1 For song #1 there are 11 options, for song #2 there are 10, for song #3 there are 9, and finally song #4 has 8 options. There are 11 songs, but only 4 will be arranged. SOLUTION #1 For song #1 there are 11 options, for song #2 there are 10, for song #3 there are 9, and finally song #4 has 8 options.

39. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists? There are 11 songs, but only 4 will be arranged. SOLUTION #1 For song #1 there are 11 options, for song #2 there are 10, for song #3 there are 9, and finally song #4 has 8 options. Therefore, there are 111098 = 7920 playlists. There are 11 songs, but only 4 will be arranged. SOLUTION #1 For song #1 there are 11 options, for song #2 there are 10, for song #3 there are 9, and finally song #4 has 8 options. Therefore, there are 111098 = 7920 playlists.

40. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists? There are 11 songs, but only 4 will be arranged. SOLUTION #2 Since there are 11 songs, we need to see how many ways to arrange 11 items and then remove all the arrangements of the last 7 songs. There are 11 songs, but only 4 will be arranged. SOLUTION #2 Since there are 11 songs, we need to see how many ways to arrange 11 items and then remove all the arrangements of the last 7 songs.

41. I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) I’m thinking about buying the album at right from iTunes for me to listen to on my drive to work. I can listen to four songs in that time. How many different playlists will be made from four songs chosen at random from this album? (Note that the playlist of songs 1-2-3-4 is different from 4-3-2-1 and so on, but no song is repeated) How many iTunes playlists? There are 11 songs, but only 4 will be arranged. SOLUTION #2 Since there are 11 songs, we need to see how many ways to arrange 11 items and then remove all the arrangements of the last 7 songs. Therefore, the number of playlists is: There are 11 songs, but only 4 will be arranged. SOLUTION #2 Since there are 11 songs, we need to see how many ways to arrange 11 items and then remove all the arrangements of the last 7 songs. Therefore, the number of playlists is:

42. Permutation Notation

43. A permutation is an arrangement of objects in a specific order. Permutations Defined

44. A permutation is an arrangement of objects in a specific order. Example: How many different starting line-ups could a coach choose for his 13-person softball team? (a starting line-up has nine players) A permutation is an arrangement of objects in a specific order. Example: How many different starting line-ups could a coach choose for his 13-person softball team? (a starting line-up has nine players) Permutations Defined

45. A permutation is an arrangement of objects in a specific order. Example: How many different starting line-ups could a coach choose for his 13-person softball team? (a starting line-up has nine players) A permutation is an arrangement of objects in a specific order. Example: How many different starting line-ups could a coach choose for his 13-person softball team? (a starting line-up has nine players) Permutations Defined

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