If total number of ways in which 9 distinct books can be distributed among ‘3’ students such that each receives at least one book and no two of them get the same number of books is K, then   is equal to 

The possible number of ways Such that each gets atleast one

$$\begin{gathered} \left(1,2,6\right)=\frac{9!}{2!6!}\left(3!\right)=1512. \\ \left(1,3,5\right)=\frac{9!}{3!5!}\left(3!\right)=3024. \\ \mathrm{and} \left(2,3,4\right)=\frac{9!}{2!3!4!}\left(3!\right)=7560 \end{gathered}$$

K=Total number of ways of distributing 9 books to 3 students such that each gets atleast one book and no two gets same number of books =k=1512+3024+7560=12096

$\boxed{\frac{k}{2016}=\frac{12096}{2016}=6}$