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      Question

      Using all the letters of the word POETRY, how many words

      start with a vowel but end with a consonant?
      A 144 Correct Answer Incorrect Answer
      B 96 Correct Answer Incorrect Answer
      C 216 Correct Answer Incorrect Answer
      D 192 Correct Answer Incorrect Answer
      E 120 Correct Answer Incorrect Answer

      Solution

      The word POETRY has two vowels – O and E.
      If a word starts and ends with a vowel, the two letters to occupy the first and the last positions can be selected and arranged in 2P2 = 2 × 1 = 2 ways.
      The remaining 4 letters can be arranged in 4! = 24 ways.
      Number of words that start and end with a vowel = 2 × 24 = 48

      If a word starts with a vowel but ends with a consonant, its first letter can be selected from O and E = 2 ways.
      Last letter can be selected from P, T, R, Y = 4 ways.
      Remaining 4 letters arranged in 4! = 24 ways.
      So total = 2 × 4 × 24 = 192

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