2024 ASRJC H1 Q8

A committee of eight members consists of one married couple named Mr and Mrs Wang, together with four other men and two other women. From the committee, a working party of five persons is to be formed.

1. In how many different ways can the working party be chosen if it must contain more men than women?[3]
2. In how many different ways can the working party be chosen if it must include Mr Wang or Mrs Wang but not both?[2]
3. The eight committee members will stand in a line to take photo. Find the probability that the committee members stand in a line with the couple next to each other.[2]