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The set S={1,2,3,…, 12} is to be partion...

The set S={1,2,3,…, 12} is to be partioned into three sets A,B, C of equal size. Thus ,
`A uu B uu C =S , A nn B = B nn C = A nn C = phi` . The number of ways to partition S is :

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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