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    Question

    A jar contains 6 pink, 2 black and 4 orange balls. If 3

    balls are chosen at random without replacement, what is the probability that all 3 balls are of one colour?
    A 11/56 Correct Answer Incorrect Answer
    B 3/44 Correct Answer Incorrect Answer
    C 6/55 Correct Answer Incorrect Answer
    D 24/5 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Probability of picking all 3 pink balls = ⁶C₃ ÷ ¹²C₃ Probability of picking all 3 black balls = ²C₃ ÷ ¹²C₃ (Note: ²C₃ = 0 since we can't choose 3 from 2) Probability of picking all 3 orange balls = ⁴C₃ ÷ ¹²C₃ Required probability = (⁶C₃ + ⁴C₃) ÷ ¹²C₃ = (20 + 4) ÷ 220 = (24/220) = 6/55

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