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A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?

Correct Answer: 186

Explanation:

When at least 2 women are included.


 


The committee may consist of 3 women, 2 men : It can be done in   4 C 3 * 6 C 2   ways


 


or, 4 women, 1 man : It can be done in   4 C 4 * 6 C 1 ways


 


or, 2 women, 3 men : It can be done in 4 C 2 * 6 C 3  ways.


 


Total number of ways of forming the committees


 


4 C 2 * 6 C 3 + 4 C 3 * 6 C 2 + 4 C 4 * 6 C 1


 


= 6 x 20 + 4 x 15 + 1x 6


 


= 120 + 60 + 6 =186


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