Question

6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is

• A. $\frac{1}{432}$
• B. $\frac{12}{431}$
• C. $\frac{1}{132}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{132}$

Total number of ways in which 6 boys and 6 girls can sit in a row = 12!

Consider 6 girls as one group, then 6 boys and one group can arrange in 7! ways.

Now, 6 girls in the group can arrange among themselves in 6!

So, the number of ways in which all the girls sit together is $7!\times 6!$

$\therefore$ P(all girls sit together)

Number of ways in which all

$=\frac{\text{girls sit together}}{\text{Total number of ways in which}}$

6 boys and 6 girls sit in a row

$=\frac{7!6!}{12!}=\frac{6\times 5\times 4\times 3\times 2\times 1}{12\times 11\times 10\times 9\times 8}=\frac{1}{132}$

Hence. the correct answer is option (c).