Question

In how many ways three girls and nine boys can be seated in two vans, each having numbers 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 1

We have 14 seats in two vans. And there are 9 boys and 3 girls. The no. of ways of arranging 12 people on 14 seats without restriction is 

¹⁴P₁₂ = 14!/2! = 7 (13!) 

Now the no. of ways of choosing back seats is 2. And the no. of ways of arranging 3 girls on adjacent seats is 2 (3!). and the no. of ways of arranging 9 boys on the remaining 11 seats is ¹¹ P₉ 

Therefore, the required number of ways 

= 2. (2.3!). 11 P₉ = 4.3!. 11! /2! = 12! 

Hence, the probability of the required event 

= 12! /7.13! = 1/91