The total number of ways of dividing mn things into nequal groups, is

The total number of ways of dividing $m n$ things into $n$ equal groups, is

A
$\frac{(m n)!}{n! n!}$
B
$\frac{(m n)!}{(n)^{m} m!}$
C
$\frac{(m n)!}{(m!)^{n!} n!}$
D
none of these

Solution:

All $n$ groups are identical and equal, each

containing $m$ things. So, required number of ways is $\frac{(m n)!}{(m!)^{n!} n!}$

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