Permutations & Combinations
Permutation Combination
nta_pyq_2025_jan
Grade 11

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:
5148
6084
4356
14950

Step-by-Step Solution

Key Concept: Once $M$ is fixed in the middle and the rest sorted, you choose $2$ letters from the $12$ letters before $M$ (A–L) and $2$ from the $13$ after (N–Z). Order is forced; only selections count.
Letters before M: A, B, $\dots$, L — $12$ letters. Letters after M: N, O, $\dots$, Z — $13$ letters. Choose $2$ from each side: $\binom{12}{2}\binom{13}{2}=66\cdot 78=5148.$ Arrangement is forced (alphabetical), so the answer is $5148.$
Correct Answer: 1

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