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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" |$\binom nk = ^n\operatorname C_k = \frac\left\{n\left(n-1\right)\ldots\left(n-k+1\right)\right\}\left\{k\left(k-1\right)\dots1\right\}$ | align="center" |$^n\operatorname P_k = n\cdot\left(n-1\right)\cdot\left(n-2\right)\cdots\left(n-k+1\right)$ |- | align="center" |Task: [[Combinations]] | align="center" |Task: [[Permutations]] |- ! rowspan=2 | With replacement | align="center" |$\binom \left\{n+k-1\right\}k = ^\left\{n+k-1\right\}\operatorname C_k = \left\{\left(n+k-1\right)! \over \left(n-1\right)!k!\right\}$ | align="center" |$n^k$ |- | align="center" |Task: [[Combinations with repetitions]] | align="center" |Task: [[Permutations with repetitions]] |}