Counting sets a Howw many solutions are there in nonnegative

(Counting sets)

a) Howw many solutions are there in nonnegative integers of a+b+c+d=10?

b) How many solutions are there in positive integers of a+b+c+d=10?

c) How many solutions are there in positive integers of a+b+c+d<=10?

Solution

a) no of solutions = (10+4-1) C _4-1 =13C₃=286