🔁 可重复组合计算器（多重组合 C(n+r−1, r)）Combinations with Repetition Calculator (Multichoose C(n+r−1, r))
计算可重复组合数 C(n+r−1, r) = (n+r−1)! / (r!(n−1)!)，即从 n 种里取 r 个且允许重复、不计顺序。用精确大整数。本地处理。Combinations with repetition C(n+r−1, r) = (n+r−1)! / (r!(n−1)!): choose r from n types with repetition, order ignored. Exact big integers. Processed locally.
使用说明与常见问题How-to & FAQ
「可重复组合计算器（多重组合 C(n+r−1, r)）」是什么？What is the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) tool?
计算可重复组合数 C(n+r−1, r) = (n+r−1)! / (r!(n−1)!)，即从 n 种里取 r 个且允许重复、不计顺序。用精确大整数。本地处理。Combinations with repetition C(n+r−1, r) = (n+r−1)! / (r!(n−1)!): choose r from n types with repetition, order ignored. Exact big integers. Processed locally.
如何使用「可重复组合计算器（多重组合 C(n+r−1, r)）」？How do I use the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) tool?
在「可重复组合计算器（多重组合 C(n+r−1, r)）」中，填写「种类数 n」、「选取数 r」等参数，结果会随输入实时计算并显示在下方。In the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)): Fill in "Types n", "Choose r"; results are recalculated instantly as you type.
和普通组合有什么区别？How does this differ from ordinary combinations?
普通组合 C(n,r) 不允许重复；可重复组合（多重组合）是 C(n+r−1, r)。例如 5 种取 3 个可重复：C(7,3)=35。Ordinary C(n,r) forbids repeats; with repetition (multichoose) it is C(n+r−1, r). Example: 5 types choose 3 with repeats: C(7,3)=35.
结果会不会太大？Can the result be huge?
可以。本页用 BigInt 精确计算，n、r 最大 1000；很大的结果会显示为很长的整数。Yes. This page uses exact BigInt; n and r go up to 1000, so large answers appear as long integers.
能举个计算实例吗？Can you show a worked example?
例如在「可重复组合计算器（多重组合 C(n+r−1, r)）」中填 种类数 n = 5，选取数 r = 3，结果区显示：C(n+r−1, r)：35For example, entering Types n = 5, Choose r = 3 in the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) gives: C(n+r−1, r): 35
哪些输入会被检查？Which inputs are validated?
「可重复组合计算器（多重组合 C(n+r−1, r)）」会检查这些输入——「种类数 n」：必须填写，须为不小于 1且不大于 1,000的整数；「选取数 r」：必须填写，须为不小于 0且不大于 1,000的整数；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 Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) checks its inputs — "Types n": required, must be at least 1 and at most 1,000 (a whole number); "Choose r": required, must be at least 0 and at most 1,000 (a whole number); 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?
「可重复组合计算器（多重组合 C(n+r−1, r)）」的设置：「种类数 n」默认 5；「选取数 r」默认 3。每次生成结果都按当前设置处理。Settings in the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) — "Types n" default 5; "Choose r" default 3. The result always uses the current settings.
计算精度如何？How precise are the results?
「可重复组合计算器（多重组合 C(n+r−1, r)）」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 Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) uses double-precision floating point (about 15–16 significant digits); some features use BigInt for large integers.
「可重复组合计算器（多重组合 C(n+r−1, r)）」免费吗？需要注册吗？Is the Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) free? Do I need an account?
「可重复组合计算器（多重组合 C(n+r−1, r)）」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 Combinations with Repetition Calculator (Multichoose C(n+r−1, r)) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.