Question

Six boys and six girls sit in a row randomly. The probability that all girls sit together is

Options

•  1/122

• 1/112

•  1/102

•  1/132

   

Answer 1

 \[\frac{1}{132}\]

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 = \[\frac{7! \times 6!}{\left( 12 \right)!} = \frac{720}{12 \times 11 \times 10 \times 9 \times 8} = \frac{1}{132}\]