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June 2006 p6 q4
2808
The diagram shows the seating plan for passengers in a minibus, which has 17 seats arranged in 4 rows. The back row has 5 seats and the other 3 rows have 2 seats on each side. 11 passengers get on the minibus.
How many possible seating arrangements are there for the 11 passengers?
How many possible seating arrangements are there if 5 particular people sit in the back row?
Solution
(i) To find the number of possible seating arrangements for the 11 passengers, we use the permutation formula \(^nP_r\), where \(n\) is the total number of seats and \(r\) is the number of passengers. Here, \(n = 17\) and \(r = 11\).