An urn contains 8 red and 5 white balls. Thre | vedclass

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(D) Total number of ways to select $3$ balls from $13$ balls is ${}^{13}C_{3} = \frac{13 	imes 12 	imes 11}{3 	imes 2 	imes 1} = 286$.The event th

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$\frac{10}{13}$

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(D) Total number of ways to select $3$ balls from $13$ balls is ${}^{13}C_{3} = \frac{13 	imes 12 	imes 11}{3 	imes 2 	imes 1} = 286$.The event that balls of both colours are drawn means we select either ($2$ red and $1$ white) or ($1$ red and $2$ white) balls.Number of ways to select $2$ red and $1$ white ball $= {}^{8}C_{2} 	imes {}^{5}C_{1} = 28 	imes 5 = 140$.Number of ways to select $1$ red and $2$ white balls $= {}^{8}C_{1} 	imes {}^{5}C_{2} = 8 	imes 10 = 80$.Total favorable outcomes $= 140 + 80 = 220$.Required probability $= \frac{220}{286} = \frac{10}{13}$.

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then,the probability that balls of both colours are drawn is

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