Vowels always together — Aptitude Question
Vowels always together: In how many ways can the letters of DETAIL be arranged so that the vowels occupy only odd… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
In how many ways can the letters of DETAIL be arranged so that the vowels occupy only odd positions?
Options
- 36
- 60
- 120
- 720
Show the answer and the worked solution
Correct answer: A. 36
Worked solution
- Odd positions are 1, 3, 5 — exactly three of them, for the three vowels.
- Vowels can be arranged in those positions in 3! = 6 ways.
- The three consonants fill the even positions in 3! = 6 ways.
- Total = 6 × 6 = 36.
Answer: 36.
The idea
Place the restricted letters first, then fill the remaining positions. Multiplying the two independent arrangements gives the answer.
Shortcut. A random arrangement puts the three vowels in the three odd places with chance 1/C(6,3) = 1/20, so the count is 720 ÷ 20 = 36.
Common trap. "720" — ignoring the restriction and counting every arrangement of DETAIL, 6!; the odd-position rule leaves only 3! × 3!.
All Permutations & Combinations questions · placement mock tests