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JEE Main 2025 Jan 22 Shift 1, Mathematics Q11: Combinations

JEE Main2025Jan 22, Shift 1Mathematics
Q.

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is 'M', is :

  1. A

    14950

  2. B

    6084

  3. C

    4356

  4. D

    5148

Solution

Once the letters are picked, the alphabetical arrangement is forced, so we are counting unordered choices subject to the constraint that M sits in the middle.

M occupies position 3. Two letters must come from (12 letters before M), and two letters from (13 letters after M).

Count .

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