JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Permutations and Combinations

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The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

(A)406
(B)130
(C)142
(D)136✓ Correct

Answer: (D)

Solution

Give each of the three children 2 apples first, using up 6 of the 21 apples. This leaves 15 apples to be distributed among 3 children with no restriction (each child can now get 0 or more).

The number of ways to distribute 15 identical apples among 3 distinct children is the number of non-negative integer solutions of

x_{1} + x_{2} + x_{3} = 15

, which is

(3 - 1 15 + 3 - 1) = (2 17)

(2 17) = \frac{17 \times 16}{2} = 136

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Single correct option

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