The set `S""=""{1,""2,""3,"" ,""12)` is to be partitioned into three sets A, B, C of equal size. Thus, `AuuBuuC""=""S ,""AnnB""=""BnnC""=""AnnC""=varphi` . The number of ways to partition S is (1) `(12 !)/(3!(4!)^3)` (2) `(12 !)/(3!(3!)^4)` (3) `(12 !)/((4!)^3)` (4) `(12 !)/((4!)^4)`

Explanation

To solve the problem of partitioning the set \( S = \{1, 2, 3, \ldots, 12\} \) into three sets \( A, B, C \) of equal size, we need to follow these steps:

### Step 1: Determine the size of each set
Since the total number of elements in set \( S \) is 12 and we need to partition it into three sets of equal size, we can calculate the size of each set as follows:
\[ \text{Size of each set} = \frac{12}{3} = 4 \]
Thus, each of the sets \( A, B, \) and \( C \) will contain 4 elements.
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