CAPF AC 2021 Q80: General Mental Ability – Quantitative Aptitude
- (a) 60
- (b) 150
- (c) 100
- (d) 120
Answer: (d) 120
Explanation
Arrangements of the letters of COVID
Given: find how many different words, with or without meaning, can be formed using the letters of the word COVID.
How to think: first check for repeated letters.
C, O, V, I and D are five different letters.
So the answer is simply the number of ways to arrange five different things.
| Position | Choices left |
|---|---|
| First letter | 5 |
| Second letter | 4 |
| Third letter | 3 |
| Fourth letter | 2 |
| Fifth letter | 1 |
Multiply: 5 × 4 × 3 × 2 × 1 = 5! = 120.
If letters repeat: divide by the factorial of each repeat.
For example, INDIA has two I's, so it gives 5!/2! = 60.
Answer: (d) 120.
Why each option is right or wrong
- (a) Incorrect. 60 would be right only if one letter appeared twice.
- (b) Incorrect. 150 does not come from any factorial of five letters.
- (c) Incorrect. 100 is a guess; the count is 5 × 4 × 3 × 2 × 1.
- (d) CORRECT. Five different letters can be arranged in 5! = 120 ways.
Key point
n different letters can be arranged in n! ways. With repeats, divide by the factorial of each repeat count. 5! = 120, 6! = 720.
Remember
Five different letters = 5! = 120 arrangements.
Common mistakes
- Dividing by 2 without checking that no letter repeats in COVID.
- Counting only meaningful words, though the question says with or without meaning.
- Adding 5 + 4 + 3 + 2 + 1 instead of multiplying the choices.
Exam tip
Educated guess: five different letters always give 5! = 120. Learn the factorials up to 6 by heart: 1, 2, 6, 24, 120, 720.
Sources
- NCERT Class XI Mathematics — Permutations and Combinations (permutations when all objects are distinct)
- R. S. Aggarwal, Quantitative Aptitude — Permutations and Combinations