From a group of 10 women and 8 men, a committee of 3 men and 3 women is to be formed. In how many ways can the committee be formed if two of men refuse to serve together
Answers
Given : a group of 10 women and 8 men
a committee of 3 men and 3 women is to be formed
To Find : Number of ways the committee can be formed if two of men refuse to serve together
Solution:
Women = 10
Men = 8
committee of 3 men and 3 women is to be formed without any restriction:
= ¹⁰C₃.⁸C₃
= 120 * 56
= 6720
committee of 3 men and 3 women is to be formed when 2 men selected who refused to work together
then 3rd man can be selected in ⁶C₁ = 6 ways
Ways = ¹⁰C₃.⁶C₁
= 120 * 6
= 720
Number of ways can the committee be formed if two of men refuse to serve together = 6720 - 720
= 6000
6000 ways the committee can be formed if two of men refuse to serve together
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