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Nov 2010 p63 q6
2798
A small aeroplane has 14 seats for passengers. The seats are arranged in 4 rows of 3 seats and a back row of 2 seats (see diagram). 12 passengers board the aeroplane.
(i) How many possible seating arrangements are there for the 12 passengers? Give your answer correct to 3 significant figures.
These 12 passengers consist of 2 married couples (Mr and Mrs Lin and Mr and Mrs Brown), 5 students and 3 business people.
(ii) The 3 business people sit in the front row. The 5 students each sit at a window seat. Mr and Mrs Lin sit in the same row on the same side of the aisle. Mr and Mrs Brown sit in another row on the same side of the aisle. How many possible seating arrangements are there?
Solution
(i) To find the number of possible seating arrangements for the 12 passengers out of 14 seats, we use permutations:
The 3 business people can be arranged in the front row in \(3! = 6\) ways.
The 5 students each sit at a window seat, which can be arranged in \(5! = 120\) ways.
Mr and Mrs Lin can sit in the same row on the same side of the aisle in \(3P2 \times 2 = 12\) ways (choosing 2 out of 3 rows and 2 ways to arrange them).
Mr and Mrs Brown can sit in another row on the same side of the aisle in \(2 \times 2 = 4\) ways.