An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. - Mathematics MCQ AIEEE 2026 | ExamTest.live

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is:

Solution & Step-by-step Explanation

Total ways to draw 3 balls out of 9 = (3 9) = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84 .Ways to draw one ball of each colour (1 red, 1 blue, 1 green) = (1 3) (1 4) (1 2) = 3 \times 4 \times 2 = 24 .Probability = \frac{24}{84} = \frac{2}{7} .

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is:

2/7

1/21

2/23

1/3

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