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alec_tronn

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**Show that (kn)! is divisible by (n!)^k ?**

## Homework Statement

Show that (kn)! is divisible by (n!)^k.

## The Attempt at a Solution

I attempted a factorization of the problem as follows:

(kn)! = (kn)*(kn-1)*(k-2)...(kn-n+1) *

((k-1)n-1)*((k-1)n-2)*((k-1)n-1)...((kn-1)n-n+1)*

((k-2)n-1)*((k-2)n-2)*((k-2)n-1)...((kn-2)n-n+1)*

.

.

.

((k-k+1)n-1)*((k-k+1)n-2)*((k-k+1)n-1)...((k-k+1)n-n+1)

Then, I wanted to factor that into: (k!)(n!)^k... which I now realize is illegal. I feel like I'm close or headed in the right direction? Any advice? Thanks a lot!

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