2025 YIJC P2 Q6

A children's game set consists of \(1\) red brick, \(2\) white bricks, \(3\) orange bricks and \(4\) blue bricks. All bricks are identical except for their colour.

1. Find the number of ways to arrange the \(10\) bricks in a row if all the orange bricks are separated.[2]

A girl plans to arrange the \(10\) bricks in \(4\) rows as shown below.

Find the number of arrangements if there are

2. no restrictions,[1]
3. exactly two orange bricks and only one white brick in the same row.[3]

All the \(10\) bricks are now numbered from \(1\) to \(10\).

4. In how many ways can the bricks be arranged in a circle so that the ones with the same colour are next to each other?[2]