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

Let first distribute 4 left gloves to four person in 4! ways. Now no one gets the corresponding right glove 

$=4!\left(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}\right)=9$

$\text{ Then number of favorable ways }=9\times 4!=218$

$\text{ Total number of ways }4!\times 4!$

$\therefore \text{ Required probability }=\frac{216}{4!\times 4!}=\frac{216}{576}=\frac{3}{8}$