Given four pair of gloves, they are distributed to four persons. Each person is given a right-handed and left-handed glove, then the probability that no person gets a pair is

Options

A. `3//8`
B. `5//8`
C. `1//4`
D. `3//4`

Answer

A

Explanation

`(a)` Let us first distribute `4` left gloves to four person in `4!` ways.
If no one gets the corresponding right glove then no. of ways `=4!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+(1)/(4!))=9`
Then number of favourble ways `=9xx4!=216`
Total number of ways `4!xx4!`
`:.` Required propability `=(216)/(4!xx4!)=(216)/(576)=(3)/(8)`