Multiple choice

Find the number of arrangements that can be made with the letters of the word "MATHEMATICS' in which the vowels occur together?

  1. $
    3 \times 8 !
    $
  2. $
    2 \times 8 !
    $
  3. $
    7 \times 8 !
    $
  4. $
    6 \times 8 !
    $
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D Correct answer
AI explanation

The word MATHEMATICS has 11 letters with 4 vowels (A, A, E, I) and 7 consonants. Treating the 4 vowels as a single unit, the 8 units can be arranged in 8! ways, and the vowels can be arranged among themselves in 4! / 2! = 12 ways. The total number of arrangements is 12 * 8! = 6 * 2 * 8!, which simplifies to 6 * 8!. The correct result is 6 * 8!.

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