Six boy and six girls sit in a row randomly.  Find the probability that

6boys and 6girls sit in a row randomly.
Total ways of their seating arrangement $=12!$

No of ways in which all the 6 girls sit together $=6!\times 7!$
(Considering all 6 girls as on person) and 6 boys as six person i.e. total 7 person.

$\therefore$Probability of all girls sitting together $=\frac{6!\times 7!}{12!}=\frac{720}{12\times 11\times 10\times 9\times 8}=\frac{1}{132}$

(ii) $\therefore$ P(the boys and girls sit alternately) $=\frac{2\times 6!\times !6!}{12!}=\frac{2\times 720}{12\times 11\times 10\times 9\times 8\times 7}=\frac{1}{462}$