Q: 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. [2]

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? [4]

(iii) If, instead, the 12 passengers are seated randomly, ﬁnd the probability that Mrs Lin sits directly

behind a student and Mrs Brown sits in the front row. [4]

Sol:

(ii)

With respect to the (Figure-1) attached.

The three businessmen can choose from the first row (indicated in blue) ways they can be arranged =

The married couple can choose from the paired seat (indicated in green) the first pair getting to choose has 3 choice the second pair has 2 choices and the pair can be considered as Mr, Mrs or Mrs, Mr so total arrangements = ( x )x( x )

With respect to the (Figure-2)

Now the students get to choose among the remaining 5 window seats (one from the dotted red box, 4 from the solid red box) now the number of ways they can be arranged =

Total no.of arrangements = x( x )x( x )x

(iii) Can be solved on similar line of grouping the cases.

~Kalyan.