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The set S""=""{1,""2,""3,"" ,""12) is...

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)`

A

`(12!)/(3!(4!)^(3))`

B

`(12!)/(3!(3!)^(4))`

C

`(12!)/((4!)^(3))`

D

`(12!)/((4!)^(4))`

Text Solution

Verified by Experts

The correct Answer is:
C
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))`.
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