A school basketball team has $10$ players, of whom $2$ are centres, $5$ are forwards and

Question

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

Accepted Answer

(a)60 (b)1693440 (c)322560

2024 YIJC H1 Q7

2024 YIJC H1 Q7