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 :
- (A)14950
- (B)6084
- (C)4356
- (D)5148✓ Correct
Answer: (D)
Solution
Fix the middle (3rd of 5) letter as M. The 12 letters A–L come before M and the 13 letters N–Z come after M in the alphabet.
Since the five chosen letters must appear in alphabetical order, once the set of 5 letters is fixed, there is only one way to arrange them alphabetically. So we only need to choose:
with M itself as the middle letter.
Number of ways:
Since the five chosen letters must appear in alphabetical order, once the set of 5 letters is fixed, there is only one way to arrange them alphabetically. So we only need to choose:
- 2 letters from the 12 letters before M, and
- 2 letters from the 13 letters after M,
with M itself as the middle letter.
Number of ways:
JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Single correct option