Arranging the letters of MANGO — Aptitude Question
Arranging the letters of MANGO: How many different arrangements can be made from the letters of the word MANGO? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 30 seconds
Question
How many different arrangements can be made from the letters of the word MANGO?
Options
- 60
- 100
- 120
- 240
Show the answer and the worked solution
Correct answer: C. 120
Worked solution
- Five distinct letters can be arranged in 5! ways.
- 5! = 120.
Answer: 120.
The idea
n distinct objects arrange in n! ways. The moment letters repeat, divide by the factorial of each repeat count.
Shortcut. MANGO has no repeated letter, so nothing divides 5! = 120; a smaller count such as 60 would need a letter to appear twice.
Common trap. 60 — stopping the product after three factors (5 × 4 × 3), which counts three-letter arrangements; all five letters are used, so 5 × 4 × 3 × 2 × 1.
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