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Prove that (mn)! Is divisible by `(n!)^(m) " and" (m!)^(n)`. |
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Answer» Number of ways of distribution of (mn) distinct objects equally among n persons `=((mn)!)/((m!)^(n)n!)xxn!=((mn)!)/((m!)^(n))`. Obviously, this value is integer. So, (mn)! Is divisible by `(m!)^(n)` Similarly, number of ways of distribution of (mn) objects equally among m persons `=((mn)!)/((n!)^(m)m!)xxm!=((mn)!)/((n!)^(m))` So, (mn)! is also divisible by `(n!)^(m)`. |
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