In how many ways, can three girls can three girls and nine boys be seated in two vans, each having numbered seats, 3 in the and 4 at the back? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in  a back row on adjacent seats?

Explanation

We have 14 seats in two vans. And there are 9 boys and 3 girls.


The number of ways of arranging 12 people on 14 seats without restriction is `^14P_(12)​​=7(13!)`


Now the number of ways of choosing back seats is 2.
And the number of ways of arranging 3 girls on adjacent seats is 2(3!).

And the number of ways of arranging 9 boys on the remaining 11 seats is`^ 11P_9`​.


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