<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: Arrange words alphabetically by counting how many permutations come before SMALL. Treat repeated letters carefully: S appears once, M once, A once, L twice. Count valid arrangements lexicographically smaller than SMALL.
<p><strong>Step 1:</strong> Identify available letters: S, M, A, L, L (where L repeats twice)</p><p><strong>Step 2:</strong> Count words starting with letters before S alphabetically:</p><p>• Words starting with A: 4!/2! = 12 (remaining letters M, S, L, L)</p><p>• Words starting with L: 4!/2! = 12 (remaining letters S, M, A, L)</p><p>• Words starting with M: 4!/2! = 12 (remaining letters S, A, L, L)</p><p><strong>Step 3:</strong> Count words starting with S but coming before SMALL:</p><p>• Starting with SA: 3! = 6 (remaining letters M, L, L)</p><p>• Starting with SL: 3! = 6 (remaining letters M, A, L)</p><p>• Starting with SM: 3! = 6 (remaining letters A, L, L)</p><p><strong>Step 4:</strong> Count words starting with SM but before SMA:</p><p>• Starting with SL: Already counted above, and SLA comes before SMA: 2! = 2 (remaining L, L)</p><p><strong>Step 5:</strong> Words starting with SMA but before SMAL:</p><p>• Starting with SMA: Next letter must be L or L. SMAL is the first arrangement.</p><p><strong>Step 6:</strong> Calculate total words before SMALL:</p><p>12 + 12 + 12 + 6 + 6 + 6 + 2 = 56</p><p><strong>Step 7:</strong> Position of SMALL = 56 + 1 = <strong>57</strong></p><p>∴ Answer: C</p>
Correct Answer: C