What is the meaning of the number $\frac{k!}{a_1!...a_n!}$?

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It says that this is the number of $k$ tuples $(i_1,...,i_k), 1\leq i_k \leq n$ where the index $v$ appears exactly $a_v$ times $(v=1,..,n, a_1+...+a_n=k)$ Can someone give me an explaination how this formula comes to place?