Find the number of ways in which 22 different books can be given to 5 students, so that two students get 5 books each and all the remaining students get 4 books each.

Answer

`(22!)/(3!2!5!(4!)^(3))`

Explanation

First divide 22 books into 5 groups of the size 5,5,4,4,4.
The number of ways is `(22!)/(3!2!(5!)^(2)(4!)^(3))`
Now, number of ways of distribution of these groups among 5 students is 5! Then total number of ways of distribution is
`(22!)/(3!2!(5!)^(2)(4!)^(3))xx5!=(22!)/(3!2!5!(4!)^(3))`