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      Question

      A bag contains 4 orange balls, 5 black balls, and 6 pink

      balls. If 3 balls are taken out randomly, what is the probability that all the three balls are not of the same colour ?
      A 421/455 Correct Answer Incorrect Answer
      B 440/433 Correct Answer Incorrect Answer
      C 450/449 Correct Answer Incorrect Answer
      D 550/331 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Number of ways in which the person can pick three balls out of 15 balls = ¹⁵C₃ = 455 Number of ways of picking 3 balls of same colour = ⁴C₃ + ⁵C₃ + ⁶C₃ = 4 + 10 + 20 = 34 Probability of picking three balls of same colour = 34 / 455 Required probability = 1 – Probability of picking three balls of same colour = 1 – 34/455 = 421/455

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