A committee of two members, consisting of one male and one female, is to be formed from a group of five men and three women. Among the women, Ms. A refuses to serve on the committee if Mr. B is included. How many different committees can be formed under these conditions?

Explanation

There are three women (A, C, E) and five men including Mr. B. Ms. A will not join the committee if Mr. B is selected, so the pair (A, B) is not allowed. For Ms. A, the committee can be formed with any of the other four men (excluding B), giving 4 options. For women C and E, there is no restriction, so each can pair with any of the five men, giving 5 options each. Therefore, the total number of possible committees is 4 (A's options) + 5 (C's options) + 5 (E's options) = 14.