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

Options

A. `(12!)/(3!(4!)^(3))`
B. `(12!)/(3!(3!)^(4))`
C. `(12!)/((4!)^(3))`
D. `(12!)/((4!)^(4))`

Answer

C

Explanation

12 different objects are to be divided into 3 groups of equal size, which are named as A,B and C.
Number of ways`=.^(12)C_(4)xx.^(8)C_(4)xx.^(4)C_(4)=(12!)/((4!)^(3))`.