套餐

排列组合计算器

输入 n（可选的元素个数）和 r（选出的元素个数）。

结果

输入数值并点击“计算”查看结果。

公式

nPr=n!(n−r)!{}_nP_r = \frac{n!}{(n - r)!}

Permutations: order matters.

nCr=n!r! (n−r)!{}_nC_r = \frac{n!}{r!\,(n - r)!}

Combinations: order does not matter.

如何使用此计算器

  1. Enter whole numbers with r no bigger than n.
  2. Press Calculate to get both counts.

例题

Choose 2 from 5

5P2 = 5 × 4 = 20 ordered arrangements.

5C2 = 20 / 2! = 10 unordered selections.

常见问题

When does order matter?

For rankings or codes (permutations). For teams or hands of cards, order doesn’t matter (combinations).

Are the answers exact?

Yes — even very large counts are computed exactly.

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