JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Permutations and Combinations

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The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is ____.

Answer: 206

Solution

Let person

i

receive

r_{i}

red pens and

b_{i}

blue pens. Then

r_{i} + b_{i} = 6

for each

i

, and

\sum r_{i} = 10

.

Since

b_{i} = 6 - r_{i}

and

b_{i} \geq 0

, we need

0 \leq r_{i} \leq 6

.

We need to count non-negative integer solutions to

r_{1} + r_{2} + r_{3} + r_{4} = 10

with

0 \leq r_{i} \leq 6

.

Without upper bound:

(4 - 1 10 + 4 - 1) = (3 13) = 286

.

Subtract cases where some

r_{i} \geq 7

: If

r_{1} \geq 7

, substitute

r_{1}^{'} = r_{1} - 7

, giving

(3 6) = 20

solutions. By symmetry, 4 such cases.

Total:

286 - 4 \times 20 = 286 - 80 = 206

JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Numerical answer

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