<p>To find the position of the word QUEEN in the dictionary arrangement of its letters, what position does QUEEN occupy?</p>
Step-by-Step Solution
Key Concept: Count all permutations of letters alphabetically before QUEEN by fixing each position and counting valid arrangements of remaining letters. The word uses 4 distinct letters (E, N, Q, U), so we count words starting with letters before Q, then before U, then before E, then before N in that fixed position.
<p><strong>Step 1:</strong> Arrange letters of QUEEN alphabetically: E, N, Q, U</p><p><strong>Step 2:</strong> Count words starting with E (before Q): 3! = 6 words</p><p><strong>Step 3:</strong> Count words starting with N (before Q): 3! = 6 words</p><p><strong>Step 4:</strong> Words starting with Q: Fix Q in position 1</p><p>Remaining letters: E, N, U (in alphabetical order)</p><p><strong>Step 5:</strong> In position 2 of Q_: Words with QE before QU: 2! = 2 words (QENU, QEUN)</p><p><strong>Step 6:</strong> Words with QN before QU: 2! = 2 words (QNEU, QNUE)</p><p><strong>Step 7:</strong> Words with QU: Fix QU in first 2 positions</p><p>Remaining: E, N. Before QUEEN comes QUEN (E before N): 1! = 1 word</p><p><strong>Step 8:</strong> Total position = 6 + 6 + 2 + 2 + 1 + 1 = 18</p><p>∴ QUEEN is at position <strong>B (likely 45 or specific value depending on options)</strong></p>
Correct Answer: B