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(C) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total ways to draw $8$ marbles from $14$ is given by ${}^{14}C_{8}$.Since ${}^{n}C_{r} = {}^{n}C_{n

Vedclass · Accepted Answer

$\frac{60}{1001}$

Vedclass · Answer

(C) Total number of marbles $= 4 + 5 + 2 + 3 = 14$.Total ways to draw $8$ marbles from $14$ is given by ${}^{14}C_{8}$.Since ${}^{n}C_{r} = {}^{n}C_{n-r}$,${}^{14}C_{8} = {}^{14}C_{6} = \frac{14 	imes 13 	imes 12 	imes 11 	imes 10 	imes 9}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 3003$.To have an equal number of marbles of each colour,we must draw $2$ marbles of each of the $4$ colours ($2$ green,$2$ blue,$2$ red,$2$ yellow).Number of favourable outcomes $= {}^{4}C_{2} 	imes {}^{5}C_{2} 	imes {}^{2}C_{2} 	imes {}^{3}C_{2}$.$= 6 	imes 10 	imes 1 	imes 3 = 180$.Required probability $= \frac{180}{3003} = \frac{60}{1001}$.

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 $8$ marbles are drawn at random,what is the probability that there are equal numbers of marbles of each colour?

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