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JAMB 2000 · UME · Q43

In how many ways can the word MATHEMATICS be arranged?

Worked solution (try it first)
  1. MATHEMATICS has 11 letters, so start with 11!11!.
  2. Three letters appear twice each: M, A and T.
  3. Swapping two equal letters gives the same word, so divide by 2!2! for each of them.
  4. So there are 11!2! 2! 2!\dfrac{11!}{2!\,2!\,2!} arrangements, option C.

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