<p>The letters of the word SMALL are arranged as in a dictionary; then the position of the word SMALL is:</p>
Step-by-Step Solution
Key Concept: Count all permutations in lexicographic order that come before the given word using combinatorial counting.
<p>The word SMALL has letters S, M, A, L, L. When arranged in dictionary order, we need to count all permutations that come before SMALL.</p><p>Letters in alphabetical order: A, L, L, M, S</p><p>Words starting with A: 4!/2! = 12</p><p>Words starting with L: 4!/2! = 12</p><p>Words starting with MA: 3! = 6</p><p>Words starting with MLA: 2! = 2</p><p>Words starting with MLAS: 1! = 1</p><p>Words starting with MLLAS: 0 (doesn't exist)</p><p>Words starting with SMAA: comes before SMALL</p><p>Words starting with SMAL (not L at end): SMALA, SMALM, SMALLS etc.</p><p>Total before SMALL = 12 + 12 + 6 + 2 + 1 + 24 + 1 = 57</p><p>∴ Position of SMALL = 58th</p>
Correct Answer: D