# Factorial problem

#### idontknow

$$\displaystyle n(!)^k$$ is divisible by $$\displaystyle n!$$
Now just prove that $$\displaystyle n(!)^k > (n!)^{(n(!)^0 -1)(n(!)^1 -1)...(n(!)^{k-2}-1)}$$

#### idontknow

The two sides have the same elements(factors).
n(!)^k has more factors , same as being greater than the left side.
Proving that it can be divided by the left side is same as proving it is greater.

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