A box contains certain number of balls of Black, White and Pink Colors in the ratio 5 : 9 : 20. If two balls are drawn randomly and probability of getting both the balls as Pink is \(\frac{390}{1139}\), then find the number of Black Balls.
Answer & explanation
Correct answer: option 1
Let the number of Black, White and Pink balls are 5X,9X and 20X respectively.
Total Number of Balls = 34X
Probability of Getting two pink Balls = \(\frac{^{20R} \mathrm{ C }_2}{^{34R} \mathrm{ C }_2}\) = \(\frac{390}{1139}\)
⇒ \(\frac{20R\;×\;(20R\;-\;1)}{34R\;×\;(34R\;-\;1)}\) = \(\frac{390}{1139}\) ⇒ On solving, R = 2Number of Black Balls ⇒ R = 2 Hence, option A is correct.