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In how any different ways can a set A of...

In how any different ways can a set `A` of `3n` elements be partitioned into 3 subsets of equal number of elements? The subsets `P ,Q ,R` form a partition if `PuuQuuR=A ,PnnR=varphi,QnnR=varphi,RnnP=varphidot`

Text Solution

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The correct Answer is:
`(3n!)/((n!)^(3)3!)`
This equivalent to dividing 3n different objects into three equal size group. Hence, number of ways is `3n!//[(n!)^(3)3!]`.
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