Mathematics · Permutations and Combinations

JEE Main 2025 — 22 January, Morning Shift — Question 11

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. Option A:

    14950

  2. Option B:

    6084

  3. Option C:

    4356

  4. Option D:

    5148

    Correct

Answer: D

Step-by-step solution

We need 5 letters with M as the middle (third) when sorted alphabetically. Choose 2 letters from the 12 before M (A to L): (122)=66\binom{12}{2}=66 ways. Choose 2 letters from the 13 after M (N to Z): (132)=78\binom{13}{2}=78 ways. Since the letters are arranged in alphabetical order once chosen, the total number of ways is 66×78=514866 \times 78 = 5148. Hence the answer is D.

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Subject
Mathematics
Chapter
Permutations and Combinations
Topic
Applications of Permuations and Combination
From all the English alphabets, five letters are chosen and are… | JEE Main 2025 PYQ with Solution · DhiX AI