Question

Four boys and three girls stand in a queue for an interview, the probability that they will be in alternate positions is

• A. $\frac{1}{34}$
• B. $\frac{1}{35}$
• C. $\frac{1}{17}$
• D. $\frac{1}{68}$

Answer 1

The correct option is B

$\frac{1}{35}$

Explanation for the correct option:

Find the probability :

Given that Four boys and three girls stand in a queue for an interview.

So total cases $=7!$ ways,

Now they will be arranged in alternate positions.

Favorable cases $=4!\times 3!$ways

(As boys can be arranged in $4!$Ways, and girls can be arranged in $3!$ways)

Therefore, the required probability

$=\frac{4!\times 3!}{7!}$ $\left[\mathbf{\because }\mathit{P}\mathit{r}\mathit{o}\mathit{b}\mathit{a}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathbf{=}\frac{\mathbf{}\mathbf{F}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{s}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{s}\mathbf{}}\right]$

$$\begin{gathered} =\frac{6}{7\times 6\times 5} \\ =\frac{\mathbf{1}}{\mathbf{35}} \end{gathered}$$

Hence, the correct option is (B).