AP Statistics Friday , 08 November 2013

1. APStatisticsFriday, 08 November 2013 • OBJECTIVETSW investigate the basics of combinatorics. • TESTSare graded. • Everyone needs a calculator.

4. CRAB NEBULA (Supernova remnant) • 10 light years across • Expanding at a rate of over 1000 kilometers / second • About 6500 light years from Earth in the constellation Taurus

5. Counting, Permutations, & Combinations

6. A counting problem asks “how many ways” some event can occur. Example 1How many three-letter codes are there using letters A, B, C, and D if no letter can be repeated? One way to solve is to list all possibilities. 24 three-letter codes

7. Example 2 An experimental psychologist uses a sequence of two food rewards in an experiment regarding animal behavior. These two rewards are of three different varieties. How many different sequences of rewards are there if each variety can be used only once in each sequence? Let the two food rewards be labeled 1 and 2. Let the three different varieties be labeled a, b, and c.

8. 1 2 a 1 b 2 1 c 2 Use a factor tree to solve, where the number of end branches is your answer. 6 ways

9. Fundamental Counting Principle Suppose that a certain procedure P can be broken into n successive ordered stages, S1, S2, . . . Sn, and suppose that S1 can occur inr1 ways. S2 can occur inr2 ways. Sncan occur inrnways. Then the number of ways P can occur is

10. Revisit Example 2 An experimental psychologist uses a sequence of two food rewards in an experiment regarding animal behavior. These two rewards are of three different varieties. How many different sequences of rewards are there if each variety can be used only once in each sequence? Using the fundamental counting principle: 3 2 = 6 ways

11. Permutations An r-permutation of a set of n elements is an orderedselection of r elements from the set of n elements ! means factorial Ex. 3! = 3∙2∙1 0! = 1

12. Example 1 How many three-letter codes are there using letters A, B, C, and D if no letter can be repeated? Note: The order does matter

13. Combinations The number of combinations of n elements taken r at a time is Order does NOT matter! Where n & r are nonnegative integers &r<n

14. Example 3How many committees of three can be selected from four people? Use A, B, C, and D to represent the people Note: Does the order matter?

15. Example 4 How many ways can the 4 call letters of a radio station be arranged if the first letter must be W or K and no letters repeat?

16. Example 5 In how many ways can our class elect a president, vice-president, and secretary if no student can hold more than one office? Replace n with the number in our class.

17. Example 6 How many five-card hands are possible from a standard deck of cards?

18. Example 7 Given the digits 5, 3, 6, 7, 8, and 9, how many 3-digit numbers can be made if the first digit must be a prime number? (Can digits be repeated?) Think of these numbers as if they were on tiles, like Scrabble. After you use a tile, you can’t use it again.

19. Example 8 In how many ways can 9 horses place 1st, 2nd, or 3rd in a race?

20. Example 9 In how many ways can a team of 9 players be selected if there are 3 pitchers, 2 catchers, 6 infielders, and 4 outfielders?

21. Assignment • WS Counting Principles #1 • Due at the beginning of the period on Monday, 11 November 2013.