permutation and combination

Question

In how may ways can 'mn' things be distributed equally among n groups   ??? plz explain clearly

Comments

'mn'  things to be distributed equally among n groups ...

It means each group will contain m things -

case 1- If  all things are of same type 

Ans - 1.

case 2- If all things are of different types 

Ans- C(mn, m) * C(m(n-1), m) * C(m (n-2), m)* ......* C( m, m)

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didnt understand :( can u be more clear

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lets m=2, n=3.

here we have to distribute mn= 6 things among n=3 groups right ..?

Since we have to distribute things equally .. so each group gets 2 things.

For first group we have 6 things to distribute .. = C(6, 2)

Now for 2nd group we are left with only 4 things ... so no of ways to give things to 2nd group = C(4,2)

Similarly now for 3rd group, we are left with only 2 things  = C(2,2).

So total no of ways = C(6,2) * C( 4,2) * C(2,2).

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thank u now i understand

Answer 1

It is permutation with repetition..

mn into n groups

= (mn)! / (m! m! ....n times * n!(n groups are similar))

= (mn)! / (m!)^n  * n!