2018 AJC MYE

Four double-decker beds are arranged in a row. Eight boys, three of whom are Andrew, Ben, and Perry, are to be allocated to these beds.

1. Find the number of ways of allocating the beds to the eight boys.[1]
2. If Perry does not want to share the same double-decker bed as Andrew, find the number of ways of allocating the beds to the eight boys.[2]
3. Besides not sharing the same double-decker bed as Andrew, Perry, who is afraid of height, has also requested to be allocated on the lower deck.Ben, who is Perry's best friend, has requested to be allocated on a lower deck bed next to Perry.Find the number of ways of allocating the beds to the eight boys based on these requests.[2]

The eight boys decide to hold a meeting at a round table with eight seats.

4. Find the number of ways of arranging the boys at the round table if Perry is to be seated next to Andrew or Ben but not between them.[3]