🔁 可重复排列Permutations with Repetition Calculator
从 n 种元素中可重复地取 r 个排成一列：nʳ 种；也可计算多重集排列 n! / (n₁! n₂! …)（例如 MISSISSIPPI 的字母排列）。结果用大整数精确计算。本地处理。Arrange r items chosen from n kinds with repetition: nʳ ways; or permutations of a multiset n! / (n₁! n₂! …), e.g. letters of MISSISSIPPI. Exact big-integer results. Processed locally.
使用说明与常见问题How-to & FAQ
「可重复排列」是什么？What is the Permutations with Repetition Calculator tool?
从 n 种元素中可重复地取 r 个排成一列：nʳ 种；也可计算多重集排列 n! / (n₁! n₂! …)（例如 MISSISSIPPI 的字母排列）。结果用大整数精确计算。本地处理。Arrange r items chosen from n kinds with repetition: nʳ ways; or permutations of a multiset n! / (n₁! n₂! …), e.g. letters of MISSISSIPPI. Exact big-integer results. Processed locally.
如何使用「可重复排列」？How do I use the Permutations with Repetition Calculator tool?
填写种类数 n 和取出个数 r，即可得到可重复排列数 nʳ；如果要算多重集的排列（如 MISSISSIPPI 的字母），在可选栏中用空格分隔填写各元素的个数。结果会随输入实时更新。Enter the kinds n and the number chosen r to get nʳ arrangements with repetition; for permutations of a multiset (such as the letters of MISSISSIPPI), enter each element's count, separated by spaces, in the optional field. The result updates as you type.
与组合的区别？vs combinations?
排列讲顺序；可重复组合数为 C(n + r - 1, r)。Permutations care about order; combinations with repetition number C(n + r - 1, r).
能举个计算实例吗？Can you show a worked example?
例如在「可重复排列」中填 种类数 n = 10，取出个数 r = 3，结果区显示：nʳ：1,000For example, entering Kinds n = 10, Chosen r = 3 in the Permutations with Repetition Calculator gives: nʳ: 1,000
哪些输入会被检查？Which inputs are validated?
「可重复排列」会检查这些输入——「种类数 n」：必须填写，须为整数；「取出个数 r」：必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Permutations with Repetition Calculator checks its inputs — "Kinds n": required, must be a whole number; "Chosen r": required; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「可重复排列」的设置：「种类数 n」默认 10；「取出个数 r」默认 3；「多重集各元素个数（可选，空格分隔）」可留空。每次生成结果都按当前设置处理。Settings in the Permutations with Repetition Calculator — "Kinds n" default 10; "Chosen r" default 3; "Multiset counts (optional, space separated)" optional. The result always uses the current settings.
计算精度如何？How precise are the results?
「可重复排列」使用 JavaScript 双精度浮点数（约 15–16 位有效数字），部分功能使用 BigInt 处理大整数。The Permutations with Repetition Calculator uses double-precision floating point (about 15–16 significant digits); some features use BigInt for large integers.
「可重复排列」免费吗？需要注册吗？Is the Permutations with Repetition Calculator free? Do I need an account?
「可重复排列」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Permutations with Repetition Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.