Question

A car will hold $2$ in the front seat and $1$ in the rear seat.

If among $6$ persons $2$ can drive, then no. of ways in which the car can be filled is?

• A. $10$
• B. $20$
• C. $30$
• D. $40$

Answer 1

The correct option is D

$40$

Finding the number of ways in which the car can be filled:

Given, a car will hold $2$ in the front seat and $1$ in the rear seat

Also, there are $6$ people out of $2$ can drive

Therefore, seat of driver can be filled in ${}^{2}C_1$ ways.

As $1$People for driving seat therefore remaining peoples are $5$, they can arrange on front seat as ${}^{5}C_1$

Now the back seat can be filled by remaining $4$ people in ${}^{4}C_1$

Therefore, total number of ways

$$\begin{gathered} ={}^{2}C_1\times {}^{5}C_1\times {}^{4}C_1 \\ =2\times 5\times 4 \\ =40 \end{gathered}$$

Number of ways in which the car can be filled is $40$.

Hence, correct option is $\mathbf{\left(}\mathbf{D}\mathbf{\right)}\mathbf{.}$