CAPF AC 2022 Q41: General Mental Ability – Quantitative Aptitude
There is a group of 5 people among which there is one couple. In how many ways can these 5 people be seated in a row having 5 chairs if the couple is to be seated next to each other?
- (a) 24
- (b) 48
- (c) 60
- (d) 120
Answer: (b) 48
Explanation
Seating a couple together
Given: 5 people, one couple among them, sit in a row of 5 chairs; the couple must sit next to each other; find the number of ways.
How to think: tie the couple together and treat them as one unit.
Then arrange the units, and finally let the two swap places.
| Step | Working | Ways |
|---|---|---|
| Units to arrange | Couple as 1 unit + 3 others = 4 units | 4! = 24 |
| Within the couple | Husband-wife or wife-husband | 2! = 2 |
| Total | 24 × 2 | 48 |
Answer: (b) 48.
Why each option is right or wrong
- (a) Incorrect. 24 forgets that the couple can swap their two seats.
- (b) CORRECT. 4! × 2! = 24 × 2 = 48 ways.
- (c) Incorrect. 60 does not come from this counting.
- (d) Incorrect. 120 is 5!, the count with no condition at all.
Key point
Objects that must stay together: treat them as one unit, arrange the units, then multiply by the arrangements inside the unit. Here 4! × 2! = 48. Never together = 5! − 48 = 72.
Remember
Together: glue them, 4! × 2 = 48.
Common mistakes
- Stopping at 4! = 24 and forgetting the two orders of the couple.
- Answering 5! = 120, ignoring the condition altogether.
- Counting only the positions of the couple and not the other three people.
Exam tip
Educated guess: the answer must be less than 120 (all arrangements) and an even multiple of 24, since the couple can swap. That is 48.
Sources
- NCERT Class XI Mathematics — Permutations and Combinations
- R. S. Aggarwal, Quantitative Aptitude — Permutations and Combinations