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The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?

Correct answer: B. 144

  • A. 720
  • B. 144
  • C. 120
  • D. 36

Explanation

MEADOWS has 3 vowels, E, A and O, and 4 consonants. Placing the vowels in the even positions 2, 4 and 6 gives 3! ways, while arranging the consonants in positions 1, 3, 5 and 7 gives 4! ways, so the total is 3! x 4! = 6 x 24 = 144 arrangements. The likely trap is option c, 120, from arranging only five letters or omitting one of the factorial factors.

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