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In how many different ways can a set of 3n elements be partitioned into 3 subsets of equal number of elements?

Isn't this case of distributing distinguishable objects and distinguishable boxes, so the answer should be $(3n)! / ((n!)^3 )$.

But answer given is $ (3n)! / (6*(n!)^3) $

Can anybody explain? Or post a link where to study all concepts of permutation and combination and counting
asked in Mathematical Logic by (193 points) | 67 views
Yeah answer given is right

We also divide with the   ( no of repetition)!

n! Repeats 3 times here
I cant understand, can you please elaborate?


Suppose we 3 element in identical boxes, so that each box contain 1 element. How many ways we can do it? Only 1 way


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0 the boxes are indistinguishable, that is why we are dividing with 6?

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