A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each colour is six times the probability of drawing two blue balls. The number of red and blue balls is the bag is:

6, 3

Let RR, BB and BR denotes the color of two balls drawn. Also, let no. of red balls be x and blue balls be y.

Given : (i) P(RR) = 5P(BB) ⇒ $\frac{{^xC}_2}{{^{x+y}C}_2}=5(\frac{{^yC}_2}{{^{x+y}C}_2})$

(ii) P(BR) = 6P(BB) ⇒ $\frac{{^xC}_1.{^yC}_1}{{^{x+y}C}_2}=6(\frac{{^yC}_2}{{^{x+y}C}_2})$

solve to get x = 6; y = 3