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      Question

      A bag contains 6 red balls, 4 green balls, and 5 orange

      balls. If three balls are drawn at random from the bag, what is the probability that all three balls are either red or orange?
      A 6/91 Correct Answer Incorrect Answer
      B 1/6 Correct Answer Incorrect Answer
      C 11/93 Correct Answer Incorrect Answer
      D 3/61 Correct Answer Incorrect Answer

      Solution

      Total probability = 15C3[: Total balls = 15]  =15! /3! ×12! =35×13=455 Subsequent probability = order of choosing all three balls either red or orange = 6C3+5C3 = (6! /3! ×3!) +(5! /3! ×2!) =20+10=30 Hence probability =30/455 =6/91.

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