Q.20 The number of three letter words, with or without meaning, which can be formed using letters of the word ‘VIRUS’ without repetition of letters is
The number of three-letter words that can be formed from the letters of “VIRUS” without repetition is 60.
Problem Breakdown
The word “VIRUS” has 5 distinct letters: V, I, R, U, S. Forming three-letter words without repetition means selecting and arranging 3 letters out of these 5, where order matters (permutations). The formula is P(5,3) = 5!/(5-3)! = 5×4×3 = 60.
Step-by-Step Calculation
- Choose the first letter: 5 options (V, I, R, U, or S).
- Choose the second letter: 4 remaining options.
- Choose the third letter: 3 remaining options.
- Total: 5×4×3 = 60 unique arrangements.
Option Analysis
| Option | Value | Correct? | Reason |
|---|---|---|---|
| (A) | 30 | No | Matches C(5,3) = 10 (combinations, order irrelevant) or half of permutations. |
| (B) | 40 | No | No logical derivation; possibly 5×4×2. |
| (C) | 60 | Yes | Exact P(5,3); verified by generating all 60 words like IRS, RIV, SUI. |
| (D) | 120 | No | Full 5! permutations of all letters, not 3-letter. |
Key Permutation Concepts
Total arrangements: First position (5 choices), second (4), third (3). Avoids common errors like combinations C(5,3) = 10 (30 with repetition mix-up). Full list generates 60 unique words (e.g., VIR, SUI, URV).
CSIR NET Exam Tips
- Recognize “words with or without meaning” as permutations.
- Distinct letters simplify to nPr.
- Practice similar: TRICK yields 60 too.
