A committee of 6 is chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. In how many ways can this be done if two particular women refuse to serve on the same committee? a. 850 b. 8700 c. 7800 d. none of these

Answer

7800

Explanation

We have 10 men and 7 women and a committee of 6 containing at least 3 men and 2 women is to be formed.

Now, let us consider the case when 2 particular women are always there in the same committee. We have to make a selection of 4 from 10 men and 5 women. In this case, to comply with the initial condition of at least 3 men and at least 2 women, we have the following cases :

Hence, the number of committees when two particular women are never together is 8610-810=7800.