<p>The letters of the word 'DELHI' are arranged in all possible ways as in a dictionary, the rank of the word 'DELHI' is</p>
Step-by-Step Solution
Key Concept: Count all words that come before the given word in lexicographic order by considering positions from left to right.
<p>To find the rank of DELHI, count all permutations that come before it alphabetically.</p><p>Words starting with D: D-E-H-I-L (remaining 4 letters). We need arrangements before DELHI.</p><p>Before DELHI: arrangements starting with letters before D (none in {D,E,H,I,L}). Then within D, letters before E give no valid words. Within DE, letters before H: E comes before H, giving 3! = 6 arrangements (DEH, DEI, DEL...). But we must count carefully.</p><p>Step-by-step: Words starting with D but with second letter before E: none. Words starting with DE but third letter before H: give 2! = 2 arrangements. Words starting with DEH but fourth letter before I: none. Words starting with DEHI before L: none. Thus rank = 1 + 2 + 2 + 1 = 6.</p>
Correct Answer: c