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 equationx1+x2+x3+x4=20where 1≤x1,x2,x3,x4≤17, and x1, x2, x3, x4 denote the number of oranges given to the four children.Hence, the required number of ways is= coefficient of x20 in x+x2+x3+…+x174= coefficient of x16 in 1+x+x2+…+x164= coefficient of x16 in 1−x174(1−x)−4= coefficient of x16 in (1−x)−4=16+4−1C16=19C3=969