Intro to Combinations and Permutations

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A combination is a way of choosing items from a group, when the order does not matter. For example, if you want to take 2 fruits for your lunch and you have 3, you will need to choose 2 fruits from 3, but you probably don't care what order you take them in.

Permutation is just a fancy word for "order", and it refers to an ordered combination. For example, let's say you're the judge of a poetry contest with different prizes for 1st, 2nd and 3rd place. In this case, order matters, so you care both about choosing the winners and ordering them. In fact, sometimes you may order an entire set of elements without even choosing them, such as if you were ranking an entire class of poets. Both these cases are known as permutations.

In a combination, you just care what was chosen, not what order it is in. So {Anna, Bill, Charlie} is the same combination as {Charlie, Anna, Bill}, but a different permutation.

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You would like to crack the code to your friend's combination lock, and wonder how many codes are possible. It consists of 3 dials with numbers on them. What is this a case of?

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