In how many ways can Rs. 16 be divided into 4 persons when none of them gets less than Rs. 3?

Answer

35

Explanation

First give Rs 3 to each of four person. Now for remaining Rs 4 we have
x+y+z+w=4
where x, y, z, w are number of rupees gained by person 1,2,3,4, respectively.
We have to find number of non-negative solutions of Eq. (1), which is `. (4+4-1)C_(4-1)= .^(7)C_(3)=35`.