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      Question

      If the letters of the word PLAYERS be arranged at

      random, what is the probability that there are exactly five letters between P and S?   
      A 7/55 Correct Answer Incorrect Answer
      B 6/49 Correct Answer Incorrect Answer
      C 8/51 Correct Answer Incorrect Answer
      D 1/42 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      S = 7! = 7 × 5 × 4 × 3 × 2 × 1 = 5040 Let E= event of getting exactly fiveletters between P and S n(E) = 5! = 120  ∴ P (E) = (n(E))/(n(S)) = (120 )/5040 =  1/42

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