In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front 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 ?

Answer

A

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 `""^(14)P_(12)=(14!)/(2!)=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 `""^(11)P_9` ways
Therefore, the required number of ways
`2.(2.3!)""^(11)P_9=(4.3!11!)/(2!)=12!`
Hence, the probability of the required event
`=(12!)/(7.131)=(1)/(91)`