A bag contains certain number of green and pink balls. The ratio of the number of green and pink balls in the bag is 7 : 5 respectively. Two balls are randomly drawn from the bag and the probability that both the balls are pink is \(\frac{1}{6}\). Find the total number of balls in the bag.

 36

Let the number of green and pink balls in the bag are 7R and 5R respectively

The probability that both the balls are pink =  \(\frac{^{5} \mathrm{ C }_2}{^{12} \mathrm{C}_2}\) = \(\frac{1}{6}\)

⇒ \(\frac{5R × (5R - 1)}{12R (12R - 1)}\) =\(\frac{1}{6}\)

⇒ R = 3

⇒ So, the total number of balls in the bag = 12× 3  = 36

Hence, option C is correct.