6.7 Permutations & Combinations. Factorial: 4! = 432*1 On calculator: math ==> PRB ==> 4 7! = 5040 Try 12!

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Presentation transcript:

6.7 Permutations & Combinations. Factorial: 4! = 4*3*2*1 On calculator: math ==> PRB ==> 4 7! = 5040 Try 12!

 Per Counting Principle: There are ten runners in a race. How many ways can you hand out a 1st, 2nd, and 3rd place prize? ____, _____, _____ 10 people can finish first. 9 people can finish second 8 different people can finish third. 10*9*8 = 720.

A ten player basketball team lines up for a photo shoot. How many ways can they be pictured? ___, ___, ___, ___, ____, ____, ____, ____, ____, ____ 10 choices, 9 choices, 8 choices, etc. 10*9*8* *1. Easier to just say 10! = 3,628,800

Permutations: n items arranged r at a time. order matters. n P r = n! (n -r)! 10 P 4 = 10! (10 - 4)! There are ten runners in a race. How many ways can 4 different prizes be given?

450 people are running a race. Prizes are awarded to the first 5 finishers. How many ways to give out a 1st, 2nd, 3rd, etc? ____, ____, ____, ____, ____ 450*449*448*447*446 = big number. Or 450 P 5 = 450! 450! ( )! 445!

Combination: Order doesn't matter. How many ways to pick three people out of 31 for an experiment? 31*30*29 is how many DISTINCT ways to pick people. Once they are picked, it doesn't matter who they are or where they stand. They serve the same purpose. You have to divide out by the 3*2*1 ways those three people can be arranged.

n C r = n! r!(n- r)! 31 C 3 = 31! 3!(31-3)!

You are CHOOSING 3 people out of 31. The top 3 finishers get to move on in a race of 8. How many groups of three can move on? 8 C 3 = 8! / 3!*5! There are 11 players on a basketball team. How many ways can 5 players be on the court? 11 C 5 = 11! / 5!*6!

How many 5 card poker hands are possible? 52 C 5 = 52! / 5!*47! How many 4 person committees can be chosen from this class of 30? 30 C 4 How many ways can a president, vice president, and treasurer be chosen from this class of 30? 30 P 3

Problems to do: pg , 17-20, 24-27, pg odd plus 18, 19, 30, 32, 40, 46-49