Question

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

• A. $10$
• B. $18$
• C. $20$
• D. $40$

Answer 1

The correct option is D $40$

Number of drivers $=$ $2$
The drivers seat can be filled in ${}^2{C}_1$ ways. i. e., $2$ ways

out of the remaining persons $=4+1=5$.

$5$ persons arrange in vacant seats in ${}^5{P}_2$ ways.
Total number of ways $=2{\times }^5{P}_2=40$