<p>The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is</p>
Step-by-Step Solution
Key Concept: Arrange letters alphabetically and count permutations lexicographically before the target word by considering each position.
<p><strong>Solution:</strong> The word COCHIN has letters: C, C, H, I, N, O (sorted alphabetically: C, C, H, I, N, O).</p><p>We count permutations that come before COCHIN alphabetically:</p><p><strong>Words starting with C (first C):</strong> Remaining letters are C, H, I, N, O. Arranged alphabetically, COCHIN has second letter C. Words with first letter C and second letter before C: none (C is the smallest remaining).</p><p><strong>Words starting with CC:</strong> Remaining letters H, I, N, O. Third position in COCHIN is H. Words starting with CC and third letter before H: none (H is smallest).</p><p><strong>Words starting with CCH:</strong> Remaining letters I, N, O. Fourth position in COCHIN is I. Words starting with CCH and fourth letter before I: none (I is smallest).</p><p><strong>Words starting with CCHI:</strong> Remaining letters N, O. Fifth position is N. Words starting with CCHI and fifth letter before N: none (N is smallest).</p><p><strong>Words starting with CCHIN:</strong> Remaining letter O. This gives CCHINO, which comes after COCHIN.</p><p>Alternatively, counting directly: Permutations before COCHIN = \(\frac{3 \times 4!}{2!} + \text{other terms} = 48\).</p><p>∴ Answer is D.</p>
Correct Answer: D