If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:

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KollegeApply · Accepted Answer

$\frac{47}{66}$ Explanation: Given, Number of white balls = 3 Number of Black balls = 4 Number of Red balls = 5 Total no. of balls (ways) = 12 Total no. of ways of drawing 2 balls out of 12 balls = 12C2 = (12!)/(10!2!) = 66 Total no. of ways of drawing 2 balls of different colours = 1 white 1 black + 1 black 1 red + 1 red 1 white = 3C1 $\times$ 4C1 + 4C1 $\times$ 5C1 + 5C1 $\times$ 3C1 = 3 $\times$ 4 + 4 $\times$ 5 + 5 $\times$ 3 = 47 So, the probability of drawing 2 balls of different colours = $\frac{47}{66}$

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