In how many ways can 8 different books be distributed among 3 students if each receives atleast 2 books?

Explanation

Since each student gets at least two books, possible groups sizes are (2,2,4) or (3,3,2).
Number of ways of dividing into groups of sizes 2,2and 4
`=(8!)/((2!)^(2)4!2!)`
Number of ways of dividing into groups of sizes 3,3,and 2
`=(8!)/((3!)^(2)2!2!)`
So, required number of distributions among three persons
`(8!)/((2!)^(2)4!2!)xx3!+(8!)/((3!)^(2)2!2!)xx3!`
`=(8!xx3!)/(2!xx2!)[(1)/(4!2!)+(1)/((3!)^(2))]`