Arranging MATHEMATICS — Aptitude Question
Arranging MATHEMATICS: How many distinct arrangements can be made of the letters of MATHEMATICS? Answer and worked solution on CodeKairo.
- Topic: Permutations & Combinations
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
How many distinct arrangements can be made of the letters of MATHEMATICS?
Options
- 4,989,600
- 5,987,520
- 9,979,200
- 39,916,800
Show the answer and the worked solution
Correct answer: A. 4,989,600
Worked solution
- 11 letters in all, with M, A and T each repeated twice.
- Arrangements = 11!/(2! 2! 2!) = 39,916,800 / 8 = 4,989,600.
Answer: 4,989,600.
The idea
Count the letters carefully first, then divide by 2! for each repeated pair. Three pairs means dividing by 8.
Shortcut. Read the options: 39,916,800 is 11! itself and 9,979,200 is 11! ÷ 4. Three repeated pairs need a divisor of 8, so the answer is half of 9,979,200: 4,989,600.
Common trap. "9,979,200" — spotting only two of the repeated pairs (usually M and A, missing the second T) and dividing 11! by 4 instead of 8.
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