🔢 二项式系数（组合数）计算器Binomial Coefficient Calculator
计算组合数 C(n, k) = n! ÷ (k!(n − k)!)，即从 n 个不同元素中取 k 个的方法数，用大整数精确计算并给出位数和科学记数法；n 最大 100,000。Calculate the binomial coefficient C(n, k) = n! ÷ (k!(n − k)!), the number of ways to choose k items from n, exactly with big integers, with the digit count and scientific notation; n up to 100,000.
使用说明与常见问题How-to & FAQ
「二项式系数（组合数）计算器」是什么？What is the Binomial Coefficient Calculator tool?
计算组合数 C(n, k) = n! ÷ (k!(n − k)!)，即从 n 个不同元素中取 k 个的方法数，用大整数精确计算并给出位数和科学记数法；n 最大 100,000。Calculate the binomial coefficient C(n, k) = n! ÷ (k!(n − k)!), the number of ways to choose k items from n, exactly with big integers, with the digit count and scientific notation; n up to 100,000.
如何使用「二项式系数（组合数）计算器」？How do I use the Binomial Coefficient Calculator tool?
在「二项式系数（组合数）计算器」中，填写「n（总数）」、「k（选取数）」等参数，结果会随输入实时计算并显示在下方。In the Binomial Coefficient Calculator: Fill in "n (total)", "k (chosen)"; results are recalculated instantly as you type.
组合数怎么算？How is C(n, k) calculated?
C(n, k) = n! ÷ (k! (n − k)!)。工具用 C(n, k) = C(n, n − k) 取较小的 k，再用大整数逐步相乘相除，每一步都是整数，结果精确。C(n, k) = n! ÷ (k! (n − k)!). The tool uses the smaller of k and n − k and multiplies and divides step by step with big integers; every step stays an integer, so the result is exact.
组合和排列有什么区别？Combination or permutation?
组合不计顺序（选 3 人组队），排列计顺序（选 3 人排名次）。排列数 P(n, k) = C(n, k) × k!。Combinations ignore order (picking a team of 3); permutations count it (ranking 3 people). P(n, k) = C(n, k) × k!.
为什么叫二项式系数？Why the name binomial coefficient?
它是 (a + b)ⁿ 展开后 aⁿ⁻ᵏbᵏ 项的系数，也是杨辉（帕斯卡）三角形第 n 行的第 k 个数。It is the coefficient of aⁿ⁻ᵏbᵏ in the expansion of (a + b)ⁿ, and entry k of row n of Pascal's triangle.
计算精度如何？How precise are the results?
「二项式系数（组合数）计算器」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 Binomial Coefficient Calculator uses double-precision floating point (about 15–16 significant digits); some features use BigInt for large integers.
「二项式系数（组合数）计算器」免费吗？需要注册吗？Is the Binomial Coefficient Calculator free? Do I need an account?
「二项式系数（组合数）计算器」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 Binomial Coefficient 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.