2025 TGM P2 Q6

A group of \(10\) people consists of \(3\) single men, \(3\) single women and \(2\) married couples. Each couple consists of a husband and wife.\n\nThe \(10\) people plan to have dinner and sit in a row to queue before entering the restaurant.

1. In how many different ways can the \(10\) people sit so that each husband and wife in a couple queue next to each other?[2]
2. In how many different ways can the \(10\) people queue so that the \(5\) men all sit next to each other, and none of the husbands sits next to his own wife?[3]

They then sit in a round table in the restaurant. In how many different ways can they be seated if

3. men and women alternate,[2]
4. the single women are separated.[2]