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      Question

      A three-lettered word is to be formed from the letters

      of the English alphabet. If the first and the last letter of the word are different vowels and the middle letter is a consonant, then in how many ways can the word be formed?
      A 420 ways Correct Answer Incorrect Answer
      B 362 ways Correct Answer Incorrect Answer
      C 440 ways Correct Answer Incorrect Answer
      D 125 ways Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      ATQ, There are 21 consonants and 5 vowels in the English alphabet. Number of ways to choose the first letter (vowel) 5C1 = 5 Number of ways to choose the second letter (consonant) = 21C1 = 21 Number of ways to choose the third letter (different vowel) = 4C1 = 4 (Since it must be different from the first vowel) Hence total number of ways = 5 × 21 × 4 = 420 ways

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