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

 

Answer 1

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 = \[\frac{396}{816} = \frac{33}{68}\]