The number of ways, in which 16 oranges can be distributed to four children such that each child get

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

Accepted Answer

Let oranges are identical then$$x_{1} + x_{2} + x_{3} + x_{4} = 16 $$and $x_{1},x_{2},x_{3},x_{4} \geq 1$or $x_{1}' + x_{2}' + x_{3}' + x_{4}' = 12$so total number of solutions are$$= \ ^{12 + 3}C_{3} = \ ^{15}C_{3} = 455$$

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