2024 YIJC H1 Q7

A school basketball team has \(10\) players, of whom \(2\) are centres, \(5\) are forwards and \(3\) are guards. A first team of \(5\) is to be chosen from the \(10\) players.

1. In how many different ways can the first team be chosen if it must include \(1\) centre, \(2\) forwards and \(2\) guards?[2]

The \(10\) players of the school basketball team stand in a line for a photo.

2. In how many different ways can the players stand in a line with no two guards next to each other?[2]

For another photo, the \(10\) players of the school basketball team stand in two rows of \(5\) players each.

3. In how many different ways can the players stand with the centres next to each other in the back row?[2]