JEE Main 2026 Jan 23 Shift 2, Mathematics Q15: Combinations

JEE Main2026Jan 23, Shift 2Mathematics

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

Solution

The oranges are identical. Let $x_{i} \geq 1$ be the number received by child $i$ , with $x_{1} + x_{2} + x_{3} + x_{4} = 16$ .

Substitute $y_{i} = x_{i} - 1 \geq 0$ : $y_{1} + y_{2} + y_{3} + y_{4} = 12$ .

Number of non-negative integer solutions $= (3 12 + 3) = (3 15) = 455$ .

Concept behind this question

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