Mathematics · Permutations and Combinations

JEE Main 2026 — 23 January, Evening Shift — Question 15

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

Answer: D

Let oranges are identical then $\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}+\mathrm{x}_{4}=16$ and

$\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3}, \mathrm{x}_{4} \geq 1$ or $x_{1}^{\prime}+x_{2}^{\prime}+x_{3}^{\prime}+x_{4}^{\prime}=12$

so total number of solutions are $={ }^{12+3} \mathrm{C}_{3}={ }^{15} \mathrm{C}_{3}=455$

Answer key and solution verified before publishing.

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