Question

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

Hint:

The key to this problem is recognizing the positions of the letters before and after 'M' in the alphabet.

Answer 1

The Correct Option is D

We are to select 5 letters with the middle letter being ‘M’. So, we must choose 2 letters from those before M and 2 letters from those after M. There are 12 letters before M and 13 letters after M. Thus, the number of ways is: \[ \binom{12}{2} \times \binom{13}{2} = \frac{12 \times 11}{2 \times 1} \times \frac{13 \times 12}{2 \times 1} = 5148 \] Thus, the answer is \( \boxed{5148} \).