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The number of ways in which mn different object can be divided equally into m groups,each containing n objects,Please Explain

+1 vote

I think this will work:

$\frac{\binom{mn}{n}*\binom{mn-n}{n} *\binom{mn-2n}{n}*...}{m!}$

Try taking balls B1 B2 B3 B4 and distribute them into 2 groups/partitions with each group containing 2 balls.

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Simplified formula here

answered by Veteran (18k points) 7 20 76
edited
@sushant can you explain why divide by m. I understood to numerator part, but divide by m???
They arent like 'm' distinct groups.

So, consider the balls example I gave above.

Case 1: I choose B1, B2 firstly and B3, B4 in the last choose.

Case 2: I chose B3, B4 firstly and then B1, B2 in the last case.

So, I counted twice the same partitionning, right?

Sorry, the denominator must be m!