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Question
An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
Options
5/84
3/9
3/7
7/17
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Solution
5/84
Three balls can be drawn randomly from nine balls in 9C3 = 84 ways.
Three balls cannot be red as there are only two red balls.
Three balls of the same colour can be drawn in the following ways :
3 blue out of a total of 3 blue balls.
The probability for which is \[\frac{^{3}{}{C}_3}{84} = \frac{1}{84}\]
3 black out of a total of 4 black balls.
The probability for which is \[\frac{^{4}{}{C}_3}{84} = \frac{4}{84}\]
Hence, required probability =\[\frac{1}{84} + \frac{4}{84} = \frac{5}{84}\]
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