In how many ways can 9 different books be distributed among three students if each receives atleast 2 books?

Explanation

If each receives atleast 2 books, then the division as shown by three diagrams.

The number of division ways for tree diagram (i), (ii) and (iii) are
`(9!)/((2!)^(2)(5!))xx(1)/(2!),(9!)/(2!3!4!) and (9!)/((3!)^(3))xx(1)/(3!)`, respectively.
Hence, the total number of ways of distribution of these groups among 3 students is
`[(9!)/((2!)^(2)(5!))xx(1)/(2!)+(9!)/(2!3!4!)+(9!)/((3!)^(3))xx(1)/(3!)]xx3!`
`=[378+1260+280]xx6`
`=11508`