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JEE 2025 Mathematics PYQ — From all the English alphabets, five letters are chosen and are a… | Mathem Solvex | Mathem Solvex

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JEE 2025 — Mathematics PYQ

JEE | Mathematics | 2025

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:

Choose the correct answer:

A.
14,950
B.
6084
C.
4356
D.
5148
(Correct Answer)

Correct Answer:

5148

Explanation

Total alphabets = 26
12 alphabets 13 alphabets
--------- M ---------

Remaining alphabets = 25
Now, arrangement in alphabetical order
$=^{12} C_{2} \times^{13} C_{2} \times 1$
$= \frac{12 \times 11}{2 \times 1} \times \frac{13 \times 12}{2 \times 1}$
=5148

Explanation

Total alphabets = 26
12 alphabets 13 alphabets
--------- M ---------

Remaining alphabets = 25
Now, arrangement in alphabetical order
$=^{12} C_{2} \times^{13} C_{2} \times 1$
$= \frac{12 \times 11}{2 \times 1} \times \frac{13 \times 12}{2 \times 1}$
=5148

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