A bag contains 6 red,5 white and 4 black ball | vedclass

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(A) Total number of balls $= 6 + 5 + 4 = 15$.Number of non-red balls $= 5 + 4 = 9$.We need to draw $2$ balls from the $9$ non-red balls.The number of

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$\frac{12}{35}$

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(A) Total number of balls $= 6 + 5 + 4 = 15$.Number of non-red balls $= 5 + 4 = 9$.We need to draw $2$ balls from the $9$ non-red balls.The number of ways to choose $2$ balls out of $15$ is ${}^{15}C_2 = \frac{15 	imes 14}{2 	imes 1} = 105$.The number of ways to choose $2$ non-red balls out of $9$ is ${}^{9}C_2 = \frac{9 	imes 8}{2 	imes 1} = 36$.The probability that none of the balls is red is $P = \frac{{}^{9}C_2}{{}^{15}C_2} = \frac{36}{105}$.Simplifying the fraction by dividing by $3$,we get $P = \frac{12}{35}$.

$A$ bag contains $6$ red,$5$ white and $4$ black balls. Two balls are drawn. The probability that none of them is red,is

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