Question

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that  both the balls are red .

Answer 1

Out of 15 balls, two balls can be drawn in ¹⁵C₂ ways.
∴  Total number of elementary events = ¹⁵C₂ = 105

Out of three red balls, two red balls can be chosen in ³C₂ ways.
∴ Favourable number of ways = ³C₂ = 3
Hence, required probability  = \[\frac{3}{105} = \frac{1}{35}\]