Permutation and CombinationMedium
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
Options
A.429
B.384
C.403
D.455
Solution
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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