A bag contains 6 white,7 red,and 5 black ball | vedclass

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(B) Total number of balls in the bag $= 6 + 7 + 5 = 18$.The number of ways to draw $3$ balls from $18$ balls is given by ${}^{18}C_3 = \frac{18 	imes

Vedclass · Accepted Answer

$\frac{5}{204}$

Vedclass · Answer

(B) Total number of balls in the bag $= 6 + 7 + 5 = 18$.The number of ways to draw $3$ balls from $18$ balls is given by ${}^{18}C_3 = \frac{18 	imes 17 	imes 16}{3 	imes 2 	imes 1} = 3 	imes 17 	imes 16 = 816$.The number of ways to draw $3$ white balls from $6$ white balls is given by ${}^{6}C_3 = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.The required probability is the ratio of favourable outcomes to total outcomes:$P = \frac{{}^{6}C_3}{{}^{18}C_3} = \frac{20}{816}$.Simplifying the fraction by dividing both numerator and denominator by $4$:$P = \frac{5}{204}$.

$A$ bag contains $6$ white,$7$ red,and $5$ black balls. If $3$ balls are drawn from the bag at random,then the probability that all of them are white is

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