Keeping the vowels together — Aptitude Question
Keeping the vowels together: In how many ways can the letters of MOTHER be arranged so that the vowels are always… Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
In how many ways can the letters of MOTHER be arranged so that the vowels are always together?
Options
- 120
- 240
- 360
- 720
Show the answer and the worked solution
Correct answer: B. 240
Worked solution
- Treating the two vowels as one block gives 5 items: [OE], M, T, H, R.
- These arrange in 5! = 120 ways.
- The block can be OE or EO: 2 ways.
- Total = 120 × 2 = 240.
Answer: 240.
The idea
Glue the letters that must stay together, arrange everything, then multiply by the internal arrangements of the block.
Shortcut. In a random order of 6 letters, two given letters sit side by side with chance 2/6 = 1/3, so 720 ÷ 3 = 240.
Common trap. "120" — gluing O and E into one block and arranging 5 items, but forgetting the block can read OE or EO.
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