Question

Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?

• A. $\frac{1}{462}$
• B. $\frac{1}{924}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is A

$\frac{1}{462}$

Explanation for the correct answer:

Finding the probability that the boys and girls sit alternatively:

Number of boys $=6$

Number of girls $=6$

Boys and girls sit in a row $=12$

Thus, the total number of ways $=12!$

Arrangement for boys and girls sit alternatively

Arrangement $1$: $G_1{B}_1{G}_2{B}_2{G}_3{B}_3{G}_4{B}_4{G}_5{B}_5{G}_6{B}_6=6!\times 6!$

Arrangement $2$: $B_1{G}_1{B}_2{G}_2{B}_3{G}_3{B}_4{G}_4{B}_5{G}_5{B}_6{G}_6=6!\times 6!$

Therefore, the favourable ways $=2·6!·6!$

The probability that the boys and girls sit alternatively$=\frac{\text{Favourable cases}}{\text{Total cases}}$

$$\begin{gathered} =\frac{2·6!·6!}{12!} \\ =\frac{1}{462} \end{gathered}$$

Therefore, option (A) is the correct answer.