<p>The number of words of four letters that can be formed from the letters of the word EXAMINATION is</p>
Step-by-Step Solution
Key Concept: We need to identify the available letters in EXAMINATION with their frequencies, then count 4-letter words considering cases: all different, exactly one pair repeated, and two pairs repeated.
<p><strong>Step 1: Identify letters in EXAMINATION</strong></p><p>E-1, X-1, A-2, M-1, I-2, N-2, T-1, O-1 (Total: 11 letters with A, I, N each appearing twice)</p><p><strong>Step 2: Distinct letters available = 8 (E, X, A, M, I, N, T, O)</strong></p><p><strong>Step 3: Count 4-letter words by cases:</strong></p><p><strong>Case 1: All 4 letters different</strong><br>Select 4 from 8 distinct letters: C(8,4) × 4! = 70 × 24 = 1680</p><p><strong>Case 2: Exactly one pair (one letter twice, two others different)</strong><br>Choose which repeated letter (A, I, or N): 3 ways<br>Choose 2 more from remaining 7 distinct: C(7,2) = 21<br>Arrangements: 4!/2! = 12<br>Total: 3 × 21 × 12 = 756</p><p><strong>Step 4: Total = 1680 + 756 = 2436</strong></p><p>∴ Answer: B</p>
Correct Answer: B