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Question

Using permutation or otherwise prove that n2!(n!)n is an integer, where n is a positive integer.

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Solution

We have n2 people, to be divided into n teams, each of which has n people.
Line up the n2 people, put the first n into a team, then the next n, and the next, and so on.
The no. of ways n2 people can be divided into n trams
(n2)!(n!)n
No. of ways is always on integer.
Therefore (n2)!(n!)n is an integers

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