For any positive integers m and n, show that
\[ C_{n,m} = \frac{(mn)!}{(m!)^n n!} \] is an integer.
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2019-02 Simplification of an expression with factorials,
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For any positive integers m and n, show that
\[ C_{n,m} = \frac{(mn)!}{(m!)^n n!} \] is an integer.