Question

Six boys and six girls sit in a row randomly.

The probability that all girls sit together is

• A. $\frac{1}{122}$
• B. $\frac{1}{112}$
• C. $\frac{1}{102}$
• D. $\frac{1}{132}$

Answer 1

The correct option is D

$\frac{1}{132}$

Total number of ways in which six boys and six girls can be seated in a row = (12)!

Taking all the six girls as one person, seven persons can be seated in a row in 7! ways.

The six girls can be arranged among themselves in 6! ways.

The number of wasy in which six boys and six girls can be seated in a row so that all the girls sit together = 7! $\times$ 6!

Required probability = $\frac{7!\times 6!}{\left(12\right)!}$

$=\frac{720}{12\times 11\times 10\times 9\times 8}=\frac{1}{132}$