Number of ways in which Rs.18 can be distributed amongst four persons such that nobody receives less than Rs.3 is

Suppose ith person receives Rs. xi; i = 1,2,3,4Then, x1+x2+x3+x4=18, where xi≥3Let yi=xi−3,i=1,2,3,4. Then,    y1+y2+y3+y4=6The total number of ways is equal to number of solutions of the above equation, which is given by  6+4−1C4−1=9C3=84.