A bag contains an assortment of blue and red balls. Two balls are drawn at random. The probability of drawing two red balls is six 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 in the bag is

9, 4

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8, 4

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3, 9

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4, 8

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Solution

The correct option is A $9, 4$
Let the number of the red balls is $x$
and number of blue balls is $y$
$∴^{x} C_{2} = 6 (^{y} C_{2}) and^{x} C_{1} .^{y} C_{1} = 6 (^{y} C_{2}) \Rightarrow^{x} C_{2} =^{x} C_{1} .^{y} C_{1} \Rightarrow \frac{x (x - 1)}{2} = x y \Rightarrow x = 2 y + 1 \Rightarrow x = 9, y = 4$

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The correct option is A 9, 4Let the number of the red balls is x and number of blue balls is y ∴xC2=6 (yC2)and xC1.yC1=6 (yC2)⇒xC2=xC1.yC1⇒x(x−1)2=xy⇒x=2y+1⇒x=9, y=4