2023 HCI P2 Q6

Eight students are shortlisted to be prize recipients for a competition. Two students are awarded the first prize and another two students are awarded the second prize.

The eight shortlisted students are to stand in a single row for a photo-taking session with a guest of honour. Find the number of different possible arrangements if the two first prize awardees must stand together while the two second prize awardees also must stand together during the session.[2]

After the photo-taking session, the eight students proceed for a tea reception and are to be seated at a round table with \(10\) identical seats. If \(4\) students are to be seated on each side of the guest of honour at the round table, find the total number of possible seating arrangements.[2]