9.6 Counting Principles Permutations Combinations.
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9.6 Counting Principles Permutations Combinations
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Transcript of 9.6 Counting Principles Permutations Combinations.
- Slide 1
- 9.6 Counting Principles Permutations Combinations
- Slide 2
- Fundamental Counting Principle If two choices happen in different ways, one choice is which pants to wear (called p ways), another choice is which shirt to wear (called s ways), the number of choices are p times s. If you wanted to include what type shoes ( called g), you would have p times s times g choices
- Slide 3
- Passwords If a password must contain one number and must have seven letters. How many different choices are there? __ __ __ __
- Slide 4
- Passwords If a password must contain one number and must have seven letters. How many different choices are there? 26 26 26 26 26 26 26 10 = 8.03 X 10 10
- Slide 5
- Permutations Permutation is the act of changing the arrangement of a given number of elements. A,B,CA,C,B B,A,CB,C,A C,A,BC,B,A
- Slide 6
- Permutations How many different ways in which to arrange 5 books? 1 st book, we have 5 choices 2 nd book, we have 4 choices 3 rd book, we have 3 choices 4 th book, we have 2 choices 5 th book, we have 1 choice By the Fundamental Counting Principle how many choices? 5 4 3 2 1= 5! = 120
- Slide 7
- Permutations The number of Permutations of n items is n! If there are n = 7 choices of toppings on a pizza, how many pizzas can be made? 7! =5040
- Slide 8
- Permutation when only wanting a limited number. 8 boxes of cereal but only have shelf space for 3 boxes. 1 st space 8 choices 2 nd space 7 choices 3 rd space 6 choices Fundamental Counting Principle 8 7 6 = 336 choices
- Slide 9
- Permutation when only wanting a limited number. Permutations of n elements taken r at a time.
- Slide 10
- Permutation when only wanting a limited number. Permutations of n elements taken r at a time.
- Slide 11
- What if you where looking at arranging the letters in race car. How many different permutations. Remember race car is a palindrome (same read from left to right or right to left). There are 7 letters with 3 repeating letters a, c and r.
- Slide 12
- Distinguishable Permutations race car
- Slide 13
- Combinations Here order is not important, in other words A,B,C and B,C,A are the same because they have the same letters.
- Slide 14
- Given 5 boxes, how many combinations can there be of 3 boxes? Box A, B, C, D, E {A,B,C} : {B,C,D} : {C,D,E} {A,B,D} : {B,C,E} {A,B,E} : {B,D,E} {A,C,D} : {A,C,E} :10 combinations {A,D,E} :