The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is [2026]

Question

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is [2026]

Smart Achievers · Accepted Answer

(3)

$Let oranges be identical, then$

$x_{1} + x_{2} + x_{3} + x_{4} = 16, and x_{1}, x_{2}, x_{3}, x_{4} \geq 1$

$or x_{1}' + x_{2}' + x_{3}' + x_{4}' = 12$

$so total number of solutions are$

$= {}^{12 + 3}C_{3} = {}^{15}C_{3} = 455$

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