<p>If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is</p>
Step-by-Step Solution
Key Concept: Count all valid 5-letter permutations that come alphabetically before SMALL by considering words starting with letters before S, then before the second M, and so on, treating repeated letters (L, L) carefully.
<p><strong>Step 1:</strong> Letters in SMALL: S, M, A, L, L (A appears once, L appears twice, others once)</p><p><strong>Step 2:</strong> Count words starting with letters before S alphabetically: A, L, M</p><p>• Starting with A: Remaining letters {S,M,L,L}. Permutations = 4!/2! = 12</p><p>• Starting with L: Remaining letters {S,M,A,L}. Permutations = 4! = 24</p><p>• Starting with M: Remaining letters {S,A,L,L}. Permutations = 4!/2! = 12</p><p><strong>Step 3:</strong> Words starting with SA (before SM): Remaining {M,L,L}. Permutations = 3!/2! = 3</p><p><strong>Step 4:</strong> Words starting with SLA (before SMA): Remaining {M,L}. Permutations = 2! = 2</p><p><strong>Step 5:</strong> Words starting with SLAL (before SLAM): Remaining {M}. Permutations = 1! = 1</p><p><strong>Step 6:</strong> Words starting with SLAM (before SMAL): Remaining {L}. Permutations = 1! = 1</p><p><strong>Step 7:</strong> Total words before SMALL = 12 + 24 + 12 + 3 + 2 + 1 + 1 = 55</p><p>∴ Position of SMALL = 55 + 1 = <strong>56</strong></p>
Correct Answer: D