Question

Out of 8 men and 10 women a committee consisting of 6 men and 5 women is to be formed. How many such committees can be formed when one particular man A refuses to be a member of the committee in which his boss Bs wife is there?

Answer 1

Total - [A and Bs wife are together)
= $\left[8M/610W/5\right]$ - $\left[7M/59W/4\right]$
A and Bs wife are there
= ${(}^8{C}_6)$.${(}^{10}{C}_5)$ - ${(}^7{C}_5)$.${(}^9{C}_4)$
= $\frac{8.7}{1.2}$.$\frac{\mathrm{10.9.8.7.6}}{\mathrm{1.2.3.4.5}}$ - $\frac{7.6}{1.2}$.$\frac{\mathrm{9.8.7.6}}{\mathrm{1.2.3.4}}$
= 7056 - 2646 = 4410.