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 number of ways in which the car can be fully occupied and driven by them, is:

 

detailed solution

Correct option is D

Two cases arise: Case 1: Both the drivers are occupying the car. In this case we have to choose 3 persons out of 5 for the remaining seats and car can be driven by any of the two drivers. Thus, in this case car can be occupied and driven in  5C3 2C1(4!)=480Case 2: Exactly one drive is occupying the car. In this case we have to choose 4 persons out of the remaining 5 people. In this case car can be occupied and driven in  5C4 2C1(4!)=240ways Thus, the required number of ways=480+240=720