If m and n are positive integers greater than or equal to 2, m > n, then (mn)! is divisible by
(m!)n
(n!)m
(m+n)!
(m−n)!
(mn)!(m!)n is the number of ways of distributing mn distinct objects in n persons equally. Hence (mn)!(m!)n is an integer
⇒(m!)n|(mn)!. Similarly (n!)m|(mn)!
Further m+n<2m≤mn⇒(m+n)!|(mn)! and m−n<m<mn
⇒(m−n)!|(mn)!