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In a car with seating capacity of exactly five persons, two persons can occupy the front seat and three persons can occupy the back seat. If amongst the seven persons, who wish to travel by this car, only two of them know driving, then the number of ways in which car can be fully occupied and driven by them.

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360

240

720

answer is A.

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Detailed Solution

Selecting one driver out of the two which can occupy the front seat in

C_{1}^{2} = 2

ways.
The left four seats can be occupied by arranging five non drivers in

P_{4}^{5} = 120

ways.
Now only three more seats are left to be occupied so that the car is filled to its capacity and can be driven therefore the five persons can be arranged as

P_{3}^{5} = 60

ways.
The total number of combination will therefore be

C_{1}^{2} (P_{4}^{5} + P_{3}^{5}) = 360

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