12 boys and 2 girls are to be seated in a row such that there are atleast 3 boys between the 2 girls. The number of ways this can be done is `lamdaxx12!`. The value of `lamda` is

Options

A. 55
B. 110
C. 20
D. 45

Answer

B

Explanation

`P_(1)`=Number of ways, the girls can sit together
`=(14-2+1)xx2!xx12! =26xx12!`
`P_(2)=`Number of ways, one boy sits between the girls
`=(14-3+1)xx2!xx12! =24xx12!`
`P_(3)`=Number of ways, two boys sit between the girls
`=(14-4+1)xx2!xx12! =22xx12!`
`therefore`Required number of ways`=(182-26-24-22)xx12!`
`thereforelamda=110" [given]"`