f(x_1 ,\cdots ,x_k ;n,p_1 ,\cdots ,p_k )=\begin{cases} \dfrac{n!}{x_1 !\cdots x_k !} p_1^{x_1} \cdots p_k^{x_k} &\text{when } \sum_{i=1}^k x_i =n \\[1ex] 0 &\mbox{上記以外} \end{cases} 条件付き確率 $$ \operatorname{P}(A\mid B)=\frac{\operatorname{P}(A \cap B)}{\operatorname{P}(B)} $$ $$ \operatorname{P}(A \cap B)= \operatorname{P}(B)\operatorname{P}(A\mid B) = \operatorname{P}(A)\operatorname{P}(B\mid A) $$