1. Chance of winning Unit 6 Probability

2. Multiplication Property of Counting  If one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur together is m·n. The principle can be extended to three or more events

3. Example 1  At a sporting good store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. How many skateboard choices does the store offer?

4. Addition Counting Principle  If the possibilities being counted can be divided into groups with no possibilities in common, then the total number of possibilities is the sum of the numbers of possibilities in each group.

5. Example 2  Every purchase made on a company’s website is given a random generated confirmation code. The code consists of 4 symbols (letters and digits). How many codes can be generated if at least one letter is used in each.

6. Finding Probabilities Using Permutations 6.2 pg. 342

7. Vocabulary  Factorials- for any positive integer n, the product of the integers from 1 to n is called n factorial and is written n!. Except 0! Which is equal to 1.

8. Examples  1. 6! = 654321 = 720 Find:  2. 10!  3. 8!

9. Vocab.  Permutations- an arrangement of objects in which order is IMPORTANT. The number of permutations of n objects is given by

10. Permutations  The number of permutations of n objects taken r at a time, where r ≤ n, is given by:  Used for the arrangement of objects in a specific order.

11. Examples 4. There are 5 students in the front row. How many ways can I call on each of them to present one of 5 problems on the board? 1 st 2 nd 3 rd 4 th 5 th 5 4 3 2 1 So, I have 54321 = 120 ways to call on them. 5 things taken 5 at a time… 5 P 5

12. Example 5. What if we were choosing 5 people from the entire class? 1 st 2 nd 3 rd 4 th 5 th 3029282726 So there are 17, 100, 720 ways to choose 5.

13. Example 6. A 3-digit number is formed by selecting from the digits 4, 5, 6, 7, 8, and 9. There is no repetition. How many numbers are formed?

14. Example 7. How many of the numbers from Example 6 will be greater than 800?

15. Example 8. How many 3 digit numbers can be formed using the digits 1, 2, 3, 4 and 5, if repetition is allowed?

16. Example 9. How many different 4 letter words can be formed from the word CALM? (Assume any combo of 4 is a real word) 10. How many different 4 letter words can be formed from the word LULL? (Assume any combo of 4 is a real word) What’s the difference in 9 and 10?

17. Permutations The number of permutations of n things, taken n at a time, with r of those things identical is: 11. How many different 4 letter words can be formed from the word BABY?

18. Homework Text book Pg. 344 2-26 even

19. Combinations Section 6.3

20. Definition  A Combination is a selection of objects in which order is NOT important. The number of combination of n objects taken r at a time, where

21. Example  How many combinations of 3 letters from a list of A, B, C, D are there?

22. Example  For your school pictures, you can choose 4 backgrounds from a list of 10. How many combinations of backdrops are possible?

23. Example  Five students from the 90 students in your class will be selected to answer a questionnaire about participating in school sports. How many groups of 5 students are possible?

24. Homework  Page 349  Numbers 2 -20 even