CAT 2021 Slot 2 · Quant · Question 1

CAT 2021 Slot 2 previous year question on Permutation and Combination, with the answer and a step-by-step solution.

Permutation and CombinationModern MathsType in the answer (TITA)Medium
The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is
Answer & solution

Answer: 1000

Handle the three identical items separately and multiply, since the choices are independent.

Balloons: give every child 4 at the start, which uses 12 and leaves 3 to be shared freely among 3 children. That is {{}_{}^{3+3-1}{C}}_{3-1}{=}^{5}{C}_{2}=10 ways.

Pencils: give every child 1 at the start, which uses 3 and leaves 3 to be shared freely: again{{}_{}^{5}{C}}_{2}=10 ways.

Erasers: 3 to be shared with no condition at all: {{}_{}^{5}{C}}_{2}=10ways.

Total =10\times 10\times 10=1000.

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