# Differences

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+ | ====== Permutations and Combinations ====== | ||

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+ | A factorial is the number of ways to arrange $k$ things in $k$ spots. | ||

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+ | $k * (k-1) * (k-2) * .. 1 = k!$ | ||

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+ | Permutations are a way in which a set or number of things can be ordered or arranged in which the order is important. | ||

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+ | Combinations are a way in which a set of things can be arranged where order doesn't matter. | ||

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+ | When we have to select $k$ things from $n$ possibilities: | ||

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+ | Permutation - order matters - no repetition = $P(n,k)=\frac{n!}{(n-k)!}$\\ | ||

+ | Permutation - order matters - yes repetition = $n^k$\\ | ||

+ | Combination - order doesn't matter - no repetition = $C(n,k)= \frac{n!}{k!(n-k)!}$\\ | ||