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?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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