# Differences

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 — permutations_and_combinations [2019/03/31 14:49] (current) 2019/01/01 18:25 paul created 2019/01/01 18:25 paul created Line 1: Line 1: + ====== Permutations and Combinations ====== + + A factorial is the number of ways to arrange $k$ things in $k$ spots. ​ + + $k * (k-1) * (k-2) * .. 1 = k!$ + + Permutations are a way in which a set or number of things can be ordered or arranged in which the order is important. + + Combinations are a way in which a set of things can be arranged where order doesn'​t matter. ​ + + When we have to select $k$ things from $n$ possibilities:​ + + 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 = $C(n,k)= \frac{n!}{k!(n-k)!}$\\
• permutations_and_combinations.txt