Question

Six boys and six girls sit in a row randomly. The probability that all girls sit together is
(a) 1/122
(b) 1/112
(c) 1/102
(d) 1/132

Answer 1

(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.
Then number of ways in which six boys and six girls can be seated in a row so that all the girls sit together = 7! × 6!
∴ Required probability = $\frac{7!\times 6!}{\left(12\right)!}=\frac{720}{12\times 11\times 10\times 9\times 8}=\frac{1}{132}$