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      Question

      In how many ways can the letters of the word "COMPUTER"

      be arranged, and what is the probability that all the vowels in these arrangements always appear together?
      A 1/56 Correct Answer Incorrect Answer
      B 4/43 Correct Answer Incorrect Answer
      C 1/42 Correct Answer Incorrect Answer
      D 9/45 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ;

      Total arrangements=8!=40320 Treat vowels as one block: Arrangements of 6 units=6!=720 Arrange vowels within the block: Arrangements of vowels=3!=6 Total arrangements where vowels are together = 6!×3!=720×6=4320 Probability that vowels are together = 4320/40320 = 1/9 Hence, Total arrangements, 40320 and Probability vowels are together = 1/9

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