In how many ways can 20 oranges be given to four children if each child should get at least one orange?
The maximum number of oranges that a child can get = 20 – 3 = 17.
Thus, the problem is equivalent to finding the number of integral solutions to the equation
where , and x1, x2, x3, x4 denote the number of oranges given to the four children.
Hence, the required number of ways is