Permutations and Combinations

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Presentation transcript:

Permutations and Combinations Section 13.2 Permutations and Combinations

Three Types of Permutations Example of (1) roll a die 5 times each roll could get 1-6 and the number could repeat Example of (2) pick a card from a deck then another and another without putting them back. We are only going to talk about these 2 for now.

Example: How many 5 digit zip codes can be created?

P is Permutation. n is number of objects P is Permutation. n is number of objects. r is the number of repetitions This notation is used when you have a permutation without repeat

This type of permutation uses a specific symbol ! The exclamation point ! Has a specific meaning in math It tells you to start with the number before it and multiply by each integer before it all the way down to 1. Example : 5! – 5•4•3•2•1 = 120 So we can use this to make a formula for permutations without repittion.

Evaluate: (a) P(6,4) P(7, 2) (c) P(40, 4) Use a calculator. If you have a group of four people that each have a different birthday, how many possible ways could this occur?

In a combination the same items in a different order are not counted again. So AB is the same as BA so these 2 are only counted once. List all the combinations of the 4 colors, red, green, yellow and blue taken 3 at a time. What is C(4, 3)? C instead of P represents a combination with 4 elements 3 times without repetition. red, green, yellow red, green, blue red, yellow, blue green, yellow, blue How many do you think? Can you come up with a formula?

Find the value of each expression. (b) C(5, 2) (c) C(n, n) (d) C(n, 0) (e) C(40, 4)

How many different committees of 4 people can be formed from a pool of 8 people? This one is a straight forward combination

How many ways can a committee consisting of 3 boys and 2 girls be formed if there are 7 boys and 10 girls eligible to serve on the committee? This one has 2 combinations put together. What do you think we need to do?

How many different words (real or imaginary) can be formed using all the letters in the word REARRANGE?

How many different vertical arrangements are there of 10 flags if 5 are white, 4 are blue and 2 are red?