Seating with one fixed — Aptitude Question
Seating with one fixed: In how many ways can 5 people be seated in a row if one particular person must sit at the… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
In how many ways can 5 people be seated in a row if one particular person must sit at the left end?
Options
- 24
- 60
- 96
- 120
Show the answer and the worked solution
Correct answer: A. 24
Worked solution
- One seat is fixed, so the other 4 arrange in 4! = 24 ways.
Answer: 24.
The idea
Fix the constrained person first, then count arrangements of the rest. Constraints always reduce the factorial.
Shortcut. By symmetry each of the 5 people sits at the left end in exactly 1/5 of the 120 orders: 120 ÷ 5 = 24.
Common trap. "120" — arranging all five with 5! and ignoring that one seat is already taken.
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