<p>How many 4-letter words, with or without meaning, can be formed out of the letters in the word LOGARITHMS, if repetition of letters is not allowed?</p>
Step-by-Step Solution
Key Concept: Since LOGARITHMS has 10 distinct letters and we need 4-letter words without repetition, we use permutations: select and arrange 4 letters from 10 available letters using P(10,4).
<p><strong>Step 1:</strong> Count distinct letters in LOGARITHMS</p><p>L-O-G-A-R-I-T-H-M-S contains 10 distinct letters (no repetition)</p><p><strong>Step 2:</strong> Determine what we need</p><p>We must form 4-letter words where order matters (different arrangements = different words) and repetition is not allowed</p><p><strong>Step 3:</strong> Apply permutation formula</p><p>Number of ways = P(10,4) = 10!/(10-4)! = 10!/6!</p><p><strong>Step 4:</strong> Calculate</p><p>P(10,4) = 10 × 9 × 8 × 7 = 5040</p><p><strong>Explanation:</strong> First position has 10 choices, second has 9 (one letter used), third has 8, fourth has 7</p><p>∴ Answer: <strong>5040</strong></p>
Correct Answer: 5040