Question

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

Answer 1

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

Out of seven white balls, one white ball can be drawn in ⁷C₁ ways; and one ball can be drawn from the rest of the other coloured (red and black) balls in ⁸C₁ ways.
∴ Favourable number of ways = ⁷C₁× ⁸C₁ = 7× 8 = 56
Hence, required probability = \[\frac{56}{105} = \frac{8}{15}\]