An urn contains 9 balls of which three are red and four are blue and 2 are green. Three balls are drawn at random without replacement from the urn the probability that the three balls have different colours are
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Probability of getting balls of all three colors is 2/7
1) Since, all the three balls have been drawn simultaneously without replacement, the outcome of one will not affect outcome of others in any way.
2) We have to get exactly three balls of three different colors.
Total red balls = 3
Ways of selecting a red ball = ³C₁ = 3
Total blue balls = 4
Ways of selecting a blue ball = ⁴C₁ = 4
Total green balls = 2
Ways of selecting a green ball = ²C₁ = 2
3) Total ways of selecting 3 balls out of 9 balls = ⁹C₃ = 84
4) Total favourable cases = 3*4*2= 24
5) Probability of getting balls of all three colors is 24/84 = 2/7
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