Permutations and Combinations · Question 1

JEE Advanced 2026 Paper 1NumericalMedium📈 Topic in 33% papers+4

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

Once the red pens ri of each person are fixed, blue pens 6 - ri are fixed (they total 24 - 10 = 14 automatically).

Count r1 + r2 + r3 + r4 = 10, 0 ri 6.

Without the upper bound: 133 = 286.

Some ri 7: put ri = 7 + ri', remaining sum 3: 4 63 = 80 (two such ri impossible).

Required = 286 - 80 = 206

Answer: 206

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