Permutations Intro to Algebra/Geometry. Does order matter? In English we use the word "combination" loosely, without thinking if the order of things is.

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Presentation transcript:

Permutations Intro to Algebra/Geometry

Does order matter? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words:

Does Order Matter? "My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad.

Does Order Matter? "The combination to the safe was 472". Now we do care about the order. "724" would not work, nor would "247". It has to be exactly 4-7-2

Permutation If the order does matter it is called a Permutation.

Types of Permutation There are basically two types of permutation: Repetition is Allowed: such as the lock above. It could be "333". No Repetition: for example the first three people in a running race. You can't be first and second.

Permutations with Repitition These are the easiest to calculate. When you have n things to choose from... you have n choices each time! When choosing r of them, the permutations are: n × n ×... (r times) (In other words, there are n possibilities for the first choice, THEN there are n possibilities for the second choice, and so on, multiplying each time.)

Permutations without Repition In this case, you have to reduce the number of available choices each time. For example, what order could 16 pool balls be in? After choosing, say, number “14” you can’t choose it again. So you’re first choice would have 16 possibilities, and your next choice would then have 15, then 14, and so on.

Example How many different ways can Adam, Katelyn, Christian, Alexander, Brian, and Zachary stand in a row?

Example There are 7 people competing in a race. How many different ways can you award a 1 st, 2 nd, and 3 rd place prize?

Example How many ways can the letters, X, F, N, L, and U be ordered. Repetition is allowed.

Example How many 4-digit numbers can be formed by rearranging the digits in the number 51,823?

Example A baby presses 4 numbers on a phone. How many different number sequences could she have dialed?