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`

Explanation

To solve the problem of partitioning a set \( A \) of \( 3n \) elements into 3 subsets of equal size, we can follow these steps:

### Step 1: Understand the Problem
We need to partition a set of \( 3n \) elements into 3 subsets \( P, Q, R \) such that each subset contains \( n \) elements. The subsets must be disjoint and their union must equal the original set \( A \).

### Step 2: Count the Total Arrangements
The total number of ways to arrange \( 3n \) distinct elements is given by \( (3n)! \).

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