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The total number of ways of dividing mn distinct objects into n equal groups is

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a
(mn)!(m!)n(n!)
b
(mn)!(n!)m(m!)
c
(mn)!m!n!
d
none of these

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detailed solution

Correct option is A

As groups are indistinguishable, the number of ways=1n! mnCm mn−mCm… mCm=1n!(mn)!m!(mn−m)!(mn−m)!m!(mn−2m)!⋯m!m!0!=1n!(mn)!(m!)n


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