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`

Answer

`((3n)!)/(6(n!)^(3))`

Explanation

The required number of ways=The number of ways in which 3n different things can be divided in 3 equal groups=The number of ways to distribute 3n different things equally among three persons `=(3n!)/(3!(n!)^(3))=(3n!)/(6(n!)^(3))`.