6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.
Correct Answer – C
(c) If all the girls sit together, then considered it as 1 group.
`therefore”Arrangement of 6 +1 = 7 person in a row is 7! and the girls interchanges their seets in 6! ways.” `
`therefore ” Required probability “=(6!7!)/(12!)=(1)/(132)`
Given there are 6 boys and 6 girls
\(\therefore\) No of ways in which 6 boys and 6 girls sitting together in a row=7!
6 girls sitting arrangement = 6!
\(\therefore\) required probability = \(\cfrac{7!\times6!}{12!}\)
= \(\cfrac1{132}\)