Question

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? Select the correct answer from above options

Answer 1

Correct Answer - A 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)`