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{|class="wikitable" |+ The number of samples of size k from n objects. With [[combinations and permutations]] generation tasks. |- ! ! Order Unimportant ! Order Important |- ! rowspan=2 | Without replacement | align="center" | \binom nk = ^n\operatorname C_k = \frac{n(n-1)\ldots(n-k+1)}{k(k-1)\dots1} | align="center" |^n\operatorname P_k = n\cdot(n-1)\cdot(n-2)\cdots(n-k+1) |- | align="center" |Task: [[Combinations]] | align="center" |Task: [[Permutations]] |- ! rowspan=2 | With replacement | align="center" | \binom {n+k-1}k = ^{n+k-1}\operatorname C_k = {(n+k-1)! \over (n-1)!k!} | align="center" |n^k |- | align="center" |Task: [[Combinations with repetitions]] | align="center" |Task: [[Permutations with repetitions]] |}