Question
A box contains 5 red, 4 blue and 3 green balls. Two
balls are drawn at random without replacement. Find the probability that the two balls are of different colours.Solution
Total balls = 5 + 4 + 3 = 12 Total ways to choose 2 balls = 12C2 = 66 Unfavourable cases: both balls same colour. Red–red: 5C2 = 10 Blue–blue: 4C2 = 6 Green–green: 3C2 = 3 Total same-colour pairs = 10 + 6 + 3 = 19 So favourable pairs (different colours) = 66 − 19 = 47 Required probability = 47/66.
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