The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

Step-by-step solution

Distributing 16 identical oranges to 4 children with each getting at least 1. Let x_i 1 for i = 1,2,3,4 and x₁+x₂+x₃+x₄ = 16 . Substituting y_i = x_i - 1 0 : y₁+y₂+y₃+y₄ = 12 . By stars and bars, number of ways = 12+3 3 = 15 3 = 15 14 13 6 = 455 .