组合与排列计算器
逐步计算组合与排列
该计算器将在给定对象总数和选取数量的情况下，求允许重复或不允许重复的排列/组合的数量。它还会从给定列表中生成 r-组合（r-排列）的列表，并展示步骤。
您的输入
求含重复元素的排列数 $$$\tilde{P}{\left(11,6 \right)}$$$。
生成由{B, A, N, A, N, A}构成的允许重复的长度为6的排列列表。
解答
公式为$$$\tilde{P}{\left(n,r \right)} = n^{r}$$$。
我们有 $$$n = 11$$$ 和 $$$r = 6$$$。
因此，$$$\tilde{P}{\left(11,6 \right)} = 11^{6} = 1771561$$$。
现在，处理列表。
统计每个元素的出现次数：B出现1次, A出现3次, N出现2次。
因此，生成的列表中的元素个数为 $$$N = \frac{6!}{1! 3! 2!} = 60$$$（计算阶乘可参见阶乘计算器）。
答案
$$$\tilde{P}{\left(11,6 \right)} = 1771561$$$
生成的列表中的元素个数为 $$$60$$$A。
生成的列表是{A, A, A, B, N, N}, {A, A, A, N, B, N}, {A, A, A, N, N, B}, {A, A, B, A, N, N}, {A, A, B, N, A, N}, {A, A, B, N, N, A}, {A, A, N, A, B, N}, {A, A, N, A, N, B}, {A, A, N, B, A, N}, {A, A, N, B, N, A}, {A, A, N, N, A, B}, {A, A, N, N, B, A}, {A, B, A, A, N, N}, {A, B, A, N, A, N}, {A, B, A, N, N, A}, {A, B, N, A, A, N}, {A, B, N, A, N, A}, {A, B, N, N, A, A}, {A, N, A, A, B, N}, {A, N, A, A, N, B}, {A, N, A, B, A, N}, {A, N, A, B, N, A}, {A, N, A, N, A, B}, {A, N, A, N, B, A}, {A, N, B, A, A, N}, {A, N, B, A, N, A}, {A, N, B, N, A, A}, {A, N, N, A, A, B}, {A, N, N, A, B, A}, {A, N, N, B, A, A}, {B, A, A, A, N, N}, {B, A, A, N, A, N}, {B, A, A, N, N, A}, {B, A, N, A, A, N}, {B, A, N, A, N, A}, {B, A, N, N, A, A}, {B, N, A, A, A, N}, {B, N, A, A, N, A}, {B, N, A, N, A, A}, {B, N, N, A, A, A}, {N, A, A, A, B, N}, {N, A, A, A, N, B}, {N, A, A, B, A, N}, {N, A, A, B, N, A}, {N, A, A, N, A, B}, {N, A, A, N, B, A}, {N, A, B, A, A, N}, {N, A, B, A, N, A}, {N, A, B, N, A, A}, {N, A, N, A, A, B}, {N, A, N, A, B, A}, {N, A, N, B, A, A}, {N, B, A, A, A, N}, {N, B, A, A, N, A}, {N, B, A, N, A, A}, {N, B, N, A, A, A}, {N, N, A, A, A, B}, {N, N, A, A, B, A}, {N, N, A, B, A, A}, {N, N, B, A, A, A}。