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Question
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red
Solution
Out of 18 balls, three balls can be drawn in 18C3 ways.
∴ Total number of elementary events = 18C3 = 816
There are six red balls out of which one red ball can be drawn in 6C1 ways.
Two balls from the remaining 12 balls can be drawn in 12C2 ways.
Therefore, one red two other coloured balls can be drawn in 6C1× 12C2 = 6 × 66 = 396 ways
∴ Favourable number of ways = 396
Hence, required probability = \[\frac{396}{816} = \frac{33}{68}\]
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