Q. A car will hold 2 in the front seat and 1 in the rear seat. If among 6 persons 2 can drive, then number of ways in which the car can be filled, is

A) 10
B) 20
C) 30
D) None of these
Explanation

(b)
Since, 2 persons can drive the car, therefore we have to select 1 from these two. This can be done in $\ ^{2}C_{1}$ways. Now, from the remaining 5 persons we have to select 2 which can be done in $\ ^{5}C_{2}$ ways.
Therefore, the required number of ways in which the car can be filled
$= \ ^{5}C_{2} \times \ ^{2}C_{1} = 10 \times 2 = 20$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.