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Question: The number of ways in which we can divide mn students equally among m groups is given by -...

The number of ways in which we can divide mn students equally among m groups is given by -

A

mn!n!\frac{mn!}{n!}

B

mn!m!n!\frac{mn!}{m!n!}

C

mn!m!(n!)m\frac{mn!}{m!(n!)^{m}}

D

None of these

Answer

mn!m!(n!)m\frac{mn!}{m!(n!)^{m}}

Explanation

Solution

Each group will have mnm\frac{mn}{m}= n students.

Also, there is no distinction between groups.

Required no. of ways = mn!(n!n!......mtimes),m!\frac{mn!}{(n!n!......mtimes),m!}

= mn!(n!)m(m!)\frac{mn!}{(n!)^{m}(m!)}