2025 EJC P2 Q5

Mary is setting up a tabletop display using \(6\) glasses, arranged around a circular tray, as shown in the diagram below. There are \(4\) different colours of glasses – Red, Blue, Green and Yellow. For each colour, Mary owns one tall and one short glass, so she has \(8\) glasses in total.

1. In how many ways can Mary arrange \(6\) of the \(8\) glasses around the circular tray, such that at least one glass of each colour is used?[3]
2. Mary decides to give away one tall glass and one short glass to support a charity drive. In how many ways can she choose the two glasses to give away?[1]
3. Mary decides to give away the red tall glass and green short glass. She now wants to arrange the remaining \(6\) glasses in a straight row, such that no two adjacent glasses are of the same colour. Find the number of different arrangements.[3]