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      Question

      How many three-letter words can be formed such that all

      letters are vowels, and no two letters are the same?
      A 100 ways Correct Answer Incorrect Answer
      B 62 ways Correct Answer Incorrect Answer
      C 22 ways Correct Answer Incorrect Answer
      D 60 ways Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      ATQ, Number of ways to choose the first letter (vowel) 5C₁  =5 Number of ways to choose the second letter (Different vowel) = 4C₁  = 4 Number of ways to choose the third letter (different from the first two vowels) = 3C₁  = 5 Hence total number of ways = 5 × 4 × 3 = 60 ways

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