(d) 1806
The required committee can be chosen in the following ways:
I. When Ms. B is a member and Mr. A refuses to serve. [Selection has to be made of 3 women from 8 women as Ms B is already there and 5 men from 6 men as Mr A is excluded]
II. When Ms B is not a member and Mr. A can serve. (Selection is to made of 4 women from 8 women as Ms. B is excluded and 5 men from 7 men)
∴ Total number of ways in which the committee can be formed.
= 8C3 × 6C5 + 8C4 × 7C5
= \(\frac{8\times7\times6}{3\times2}\times6\) + \(\frac{8\times7\times6\times5}{4\times3\times2}\) x \(\frac{7\times6}{2}\)
= 56 × 6 + 70 × 21 = 336 + 1470 = 1806.