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(A) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total number of ways to draw $4$ marbles from $14$ is given by ${}^{14}C_{4}$.${}^{14}C_{4} = \frac

Vedclass · Accepted Answer

$\frac{10}{1001}$

Vedclass · Answer

(A) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total number of ways to draw $4$ marbles from $14$ is given by ${}^{14}C_{4}$.${}^{14}C_{4} = \frac{14 	imes 13 	imes 12 	imes 11}{4 	imes 3 	imes 2 	imes 1} = 1001$.Number of ways to choose $2$ blue marbles from $5$ blue marbles is ${}^{5}C_{2} = \frac{5 	imes 4}{2 	imes 1} = 10$.Number of ways to choose $2$ red marbles from $2$ red marbles is ${}^{2}C_{2} = 1$.Total number of favourable outcomes $= {}^{5}C_{2} 	imes {}^{2}C_{2} = 10 	imes 1 = 10$.Required probability $= \frac{	ext{Favourable outcomes}}{	ext{Total outcomes}} = \frac{10}{1001}$.

Study the given information carefully to answer the question that follows. An urn contains $4$ green,$5$ blue,$2$ red,and $3$ yellow marbles. If $4$ marbles are drawn at random,what is the probability that $2$ are blue and $2$ are red?

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