A bag contains 4 white,5 red,and 6 blue balls | vedclass

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(C) Total number of balls $= 4 + 5 + 6 = 15$.The total number of ways to draw $3$ balls from $15$ balls is given by ${}^{15}C_{3}$:${}^{15}C_{3} = \fr

Vedclass · Accepted Answer

$\frac{2}{91}$

Vedclass · Answer

(C) Total number of balls $= 4 + 5 + 6 = 15$.The total number of ways to draw $3$ balls from $15$ balls is given by ${}^{15}C_{3}$:${}^{15}C_{3} = \frac{15 	imes 14 	imes 13}{3 	imes 2 	imes 1} = 5 	imes 7 	imes 13 = 455$.The number of ways to draw $3$ red balls from $5$ red balls is given by ${}^{5}C_{3}$:${}^{5}C_{3} = \frac{5 	imes 4 	imes 3}{3 	imes 2 	imes 1} = 10$.The probability $P(E)$ of drawing $3$ red balls is the ratio of the number of favourable outcomes to the total number of outcomes:$P(E) = \frac{10}{455} = \frac{2}{91}$.

$A$ bag contains $4$ white,$5$ red,and $6$ blue balls. Three balls are drawn at random. What is the probability that all of them are red?

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