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We say \(P(n,k)\) counts permutations, and \({n \choose k}\) counts combinations. The formulas for each are very similar, there is just an extra \(k!\) in the denominator of \({n \choose k}\text{.}\) That extra \(k!\) accounts for the fact that \({n \choose k}\) does not distinguish between the different orders that the \(k\) objects can appear in. We are just selecting (or choosing) the \(k\) objects, not arranging them. Perhaps “combination” is a misleading label. We don't mean it like a combination lock (where the order would definitely matter). Perhaps a better metaphor is a combination of flavors — you just need to decide which flavors to combine, not the order in which to combine them.

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