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      Question

      If the letters of the word HORIZON be arranged at

      random, what is the probability that all the vowels are together?
      A 5/7 Correct Answer Incorrect Answer
      B 2/9 Correct Answer Incorrect Answer
      C 1/7 Correct Answer Incorrect Answer
      D 1/8 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      S = 7!/2! = (7 × 6 × 5 × 4 × 3 × 2 × 1 )/(2 × 1)= 2520 Let E= event of getting all vowels are together n(E) = (5!x3! )/2! = 360 ∴ P (E) = (n(E))/(n(S)) = 360/2520 = 1/7

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