A box contains 5 green,4 yellow,and 3 white m | vedclass

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(D) Total number of marbles $= 5 + 4 + 3 = 12$.The number of ways to choose $3$ marbles out of $12$ is given by $^{12}C_{3} = \frac{12 	imes 11 	ime

Vedclass · Accepted Answer

$\frac{41}{44}$

Vedclass · Answer

(D) Total number of marbles $= 5 + 4 + 3 = 12$.The number of ways to choose $3$ marbles out of $12$ is given by $^{12}C_{3} = \frac{12 	imes 11 	imes 10}{3 	imes 2 	imes 1} = 220$.The number of ways to choose $3$ green marbles is $^{5}C_{3} = ^{5}C_{2} = \frac{5 	imes 4}{2 	imes 1} = 10$.The number of ways to choose $3$ yellow marbles is $^{4}C_{3} = ^{4}C_{1} = 4$.The number of ways to choose $3$ white marbles is $^{3}C_{3} = 1$.The total number of ways to choose $3$ marbles of the same colour is $10 + 4 + 1 = 15$.The probability of choosing $3$ marbles of the same colour is $\frac{15}{220} = \frac{3}{44}$.The probability that they are not of the same colour is $1 - \frac{3}{44} = \frac{41}{44}$.

$A$ box contains $5$ green,$4$ yellow,and $3$ white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour?

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