A bag contains b blue balls and r 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 color is six times the probability of drawing two blue balls. Then

Let the number of red and blue balls be r and b, respectively Then, the probability of drawing two red balls isp1= rC2C2   r+b=r(r−1)(r+b)(r+b−1)The probability of drawing two blue balls isp2= bC2 r+bC2=b(b−1)(r+b)(r+b−1)The probability of drawing one red and one blue ball isp3=  rC1×bC1C2   r+b=2br(r+b)(r+b−1)By hypothesis, p1 = 5p2 and p3 = 6p2.Therefore,r(r−1)=5b(b−1) and 2br=6b(b−1)⇒ r=6,b=3