Permutations and Combinations PSSA Unit. Permutations A permutation of the letters abc is all of their possible arrangements: abc acb bac bca cab cba.

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Presentation transcript:

Permutations and Combinations PSSA Unit

Permutations A permutation of the letters abc is all of their possible arrangements: abc acb bac bca cab cba

Permutations Permutation: Choosing r objects without repetition from n different objects such that ORDER matters is called a permutation.

For Example How many different ways can you arrange the letters in the word: WHO THINK: How many options do you have for the first spot? How many options do you have for the second spot once you already chose a letter for the first spot?

Note: What's a factorial? A factorial is written using an exclamation point - for example, 10 factorial is written 10! - and means multiply 10 times 9 times 8 times 7... all the way down to 1.

Factorial * The previous example can be solved using factorials.

Practice: 10! 8! 6! 8! - 5! 2! + 7!

Something to Remember! 0! = 1 ** Memorize this!

Permutations are used when ORDER matters. Does it matter what you pick first? Or second? Will the first pick affect the second pick?

Combinations In permutations, the order is all important - - abc is different from bca. In combinations we are concerned only that a, b, and c have been selected. abc and bca are the same combination. Here are all the combinations of abcd taken three at a time: abc abd acd bcd.

Formula Choosing r objects without repetition from n different objects such that order DOES NOT matter is called a combination.

For Example How many 5 person teams could be made from 20 students?

Example A man has a silver dollar, a half-dollar, a quarter, a dime, a nickel and a penny in his pocket. If he reaches into his pocket and pulls out 3 coins, how many different sums may he have? ** Order does not matter!

Example * How many different ways can your rearrange the word MATH? (order does matter!)

Example There are 5 girls in a beauty contest. How many different ways could the finalists be placed?

Example There are 30 boys in the class. How many different teams of 3 could we make?

Example Two girls and their dates go to the drive-in, and each wants a different flavored ice cream cone. The drive-in has 24 flavors of ice cream. How many combinations of flavors may be chosen among the four of them if each one selects one flavor?

Example We want to paint three rooms in a house, each a different color, and we may choose from seven different colors of paint. How many color combinations are possible for the three rooms?

Example How many ways can a committee of 3 be selected from 7 people, A, B, C, D, E, F, G so that there is a president, a vice-president, and a secretary?