1. How much should I invest?
I got the perfect investment offer. For the last 10 weeks I received a share recommendation from a fund manager, telling me whether a stock’s price would rise or fall over the next week. After ten weeks, all the recommendations were proved right. So, he predicted the future 10 times in a row. There is only a one-in-a-thousand chance that the result is down to luck. I think this guy is a genius. I plan to invest all my kids’ college money. What do you think?

2. The Math

3. This is a well-known scam
This is a well-known scam. The promoter sends out 100,000 s, picking a stock at random. Half the recipients are told that the stock will rise; half that it will fall. After the first week, the 50,000 who received the successful recommendation will get a second ; those that received the wrong information will be dropped from the list. And so on for ten weeks. At the end of the period, just by the law of averages, there should be 98 punters convinced of the manager’s genius and ready to entrust their savings

4. The Math

5. WARMUP Lesson 10.1, For use with pages 682-689
Evaluate the expression. Hint: NO Calculator 1.
ANSWER
120 2.
ANSWER
7/6
3. The number of choices Meghan has for displaying her trophies is represented by the expression a • b. If a = 4 and b = 3, how many choices does Meghan have?
ANSWER 12
4. How many different 4-digit bank pin numbers are there?
ANSWER
10,000

6. 10.1 Notes - Counting Principal & Permutations
Fictitious Vampires Duke it Out

7. Objective -To count the number of ways an
event can happen.

8. How many possible 7-digit phone numbers are there if the
first digit cannot be 0 or 1?

9. A multiple choice test has 6 questions with 5 choices each.
In how many ways can you complete the test?

10. 3 4 3 5 5 2 How many three-digit numbers greater than 500 can be
formed from the digits 1, 2, 5, 7 and 9 if no repetition is allowed? 3 4 3
5,7,9
How many positive three-digit even numbers can be
formed without using the digits 0, 1, 2, 3 or 4? 5 5 2
5-9
5-9
6,8

11. A certain state has license plates that are made of four numbers followed by two letters? How many different license plates are possible if no repeated letters or numbers are allowed?

12. !

13. Say “Factorial” When you see “. ”, say Factorial
Say “Factorial” When you see “!”, say Factorial. It means to multiply that number by all the positive integers less than it. Your calculator has a “button” for it. I suggest you find it. Graphing calculators, look under “Math”

14. Permutation- is an ordering of n objects.
How many permutations are there for the letters in the
word CAT?
CAT, CTA, ACT, ATC, TCA, TAC = 6
How many permutations are there for the letters in the
word CAT?

15. There are 9 songs on your MP3 player
There are 9 songs on your MP3 player. In how many different ways could you listen to these songs?
If you only had time to listen to 3 of the 9 songs on your MP3 player, how many different ways could you listen to these 3 songs?

16. In how many different ways can the letters in the word TRIANGLE be arranged?
How many different ways could 10 runners finish in first, second and third place?

17. Find the number of permutations of 7 objects taken 4 at a time.

18. Find the number of permutations for the letters in the
word STREET.

19. Find the number of permutations for the letters in the
word MATHEMATICS.
Find the number of permutations for the letters in the
word SLEEPLESS.

20. By Definition… Write it down!!!!
0! = 1

21. Do this one!!!! EXAMPLE 1 Use a tree diagram Snowboarding
A sporting goods store offers 3 types of snowboards (all-mountain, freestyle, and carving) and 2 types of boots (soft and hybrid). How many choices does the store offer for snowboarding equipment?
SOLUTION
Draw a tree diagram and count the number of branches.

22. EXAMPLE 1
Use a tree diagram
ANSWER
The tree has 6 branches. So, there are 6 possible choices.

23. EXAMPLE 2
Use the fundamental counting principle
Photography
You are framing a picture. The frames are available in 12 different styles. Each style is available in 55 different colors. You also want blue mat board, which is available in 11 different shades of blue. How many different ways can you frame the picture?

24. EXAMPLE 2
Use the fundamental counting principle
SOLUTION
You can use the fundamental counting principle to find the total number of ways to frame the picture. Multiply the number of frame styles (12), the number of frame colors (55), and the number of mat boards (11).
Number of ways =
= 7260
ANSWER
The number of different ways you can frame the picture is 7260.

25. EXAMPLE 3
Use the counting principle with repetition
License Plates
The standard configuration for a Texas license plate is 1 letter followed by 2 digits followed by 3 letters.
How many different license plates are possible if letters and digits can be repeated?
How many different license plates are possible if letters and digits cannot be repeated?

26. EXAMPLE 3
Use the counting principle with repetition
SOLUTION
There are 26 choices for each letter and 10 choices for each digit. You can use the fundamental counting principle to find the number of different plates.
Number of plates =
= 45,697,600
ANSWER
With repetition, the number of different license plates is 45,697,600.

27. EXAMPLE 3
Use the counting principle with repetition
If you cannot repeat letters there are still 26 choices for the first letter, but then only 25 remaining choices for the second letter, 24 choices for the third letter, and 23 choices for the fourth letter. Similarly, there are 10 choices for the first digit and 9 choices for the second digit. You can use the fundamental counting principle to find the number of different plates.
Number of plates =
= 32,292,000
ANSWER
Without repetition, the number of different license plates is 32,292,000.

28. GUIDED PRACTICE
for Examples 1, 2 and 3
SPORTING GOODS The store in Example 1 also offers 3 different types of bicycles (mountain, racing, and BMX) and 3 different wheel sizes (20 in., 22 in., and 24 in.). How many bicycle choices does the store offer?
9 bicycles
ANSWER

29. GUIDED PRACTICE
for Examples 1, 2 and 3
WHAT IF? In Example 3, how do the answers change for the standard configuration of a New York license plate, which is 3 letters followed by 4 numbers?
ANSWER
The number of plates would increase to 175,760,000.
The number of plates would increase to 78,624,000.

30. EXAMPLE 4
Find the number of permutations
Olympics
Ten teams are competing in the final round of the Olympic four-person bobsledding competition.
In how many different ways can the bobsledding teams finish the competition? (Assume there are no ties.)
In how many different ways can 3 of the bobsledding teams finish first, second, and third to win the gold, silver, and bronze medals?

31. EXAMPLE 4
Find the number of permutations
SOLUTION
There are 10! different ways that the teams can finish the competition.
10! =
= 3,628,800
Any of the 10 teams can finish first, then any of the remaining 9 teams can finish second, and finally any of the remaining 8 teams can finish third. So, the number of ways that the teams can win the medals is:
= 720

32. GUIDED PRACTICE
for Example 4
WHAT IF? In Example 4, how would the answers change if there were 12 bobsledding teams competing in the final round of the competition?
The number of ways to finish would increase to 479,001,600.
ANSWER
The number of ways to finish would increase to 1320.

33. EXAMPLE 5
Find permutations of n objects taken r at a time
Music
You are burning a demo CD for your band. Your band has 12 songs stored on your computer. However, you want to put only 4 songs on the demo CD. In how many orders can you burn 4 of the 12 songs onto the CD?
SOLUTION
Find the number of permutations of 12 objects taken 4 at a time.
( 12 – 4 )!
12P4 =
12!
= 11,880 8!
479,001,600
40,320
ANSWER
You can burn 4 of the 12 songs in 11,880 different orders.

34. GUIDED PRACTICE
for Example 5
Find the number of permutations.
5P3
= 60
ANSWER
4P1
= 4
ANSWER
8P5
= 6720
ANSWER

35. GUIDED PRACTICE
for Example 5
Find the number of permutations.
12P7
= 3,991,680
ANSWER

36. EXAMPLE 6
Find permutations with repetition
Find the number of distinguishable permutations of the letters in
MIAMI and
TALLAHASSEE.
SOLUTION
MIAMI has 5 letters of which M and I are each repeated 2 times. So, the number of distinguishable permutations is:
= 30
2! 2! 5! =
120

37. EXAMPLE 6
Find permutations with repetition
TALLAHASSEE has 11 letters of which A is repeated 3 times, and L, S, and E are each repeated 2 times. So, the number of distinguishable permutations is:
3! 2! 2! !
11! =
39,916,800
= 831,600

38. GUIDED PRACTICE
for Example 6
Find the number of distinguishable permutations of the letters in the word.
MALL 12
ANSWER

39. GUIDED PRACTICE
for Example 6
Find the number of distinguishable permutations of the letters in the word.
KAYAK 30
ANSWER

40. GUIDED PRACTICE
for Example 6
Find the number of distinguishable permutations of the letters in the word.
CINCINNATI
50,400
ANSWER

41. 10.1 Assignment
10.1: 3 OR 5 (Tree Diagrams – look at example 1 in the book and check your answer in the back), EOO, 65 (WP in the back), 73,75
Team Count!!