Two boys are playing a game in which they have to pick balls out of a bag. The bag contains 4 red, 3 green, 2 blue and 5 black balls. If one of the boy draws four balls at random, what is the probability that two are red and two are blue?
Correct Answer: Option A
Since there are 4 red, 3 green, 2 blue and 5 black balls in the bag, there are a total of 14 balls in the bag.
4 balls are drawn at random; therefore exhaustive number of cases = 14C4
Total cases are = 14C4 = (14 × 13 × 12 × 11)/(1 × 2 × 3 × 4) = 1001
Now we need to find the case where two are red and two are blue = 4C2 × 2C2
= 6 × 1 = 6
Therefore the required probability = 6/1001
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