A bag contains 10 identical pens,of which 4 a | vedclass

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(C) Total number of pens $= 10$. Number of red pens $= 4$. Number of blue pens $= 6$. We need to select $3$ pens out of $10$. The total number of ways

Vedclass · Accepted Answer

$\frac{1}{6}$

Vedclass · Answer

(C) Total number of pens $= 10$. Number of red pens $= 4$. Number of blue pens $= 6$. We need to select $3$ pens out of $10$. The total number of ways to choose $3$ pens is given by ${}^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$. The number of ways to choose $3$ blue pens out of $6$ is given by ${}^{6}C_3 = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$. Therefore,the required probability $P = \frac{{}^{6}C_3}{{}^{10}C_3} = \frac{20}{120} = \frac{1}{6}$. Hence,option $C$ is correct.

$A$ bag contains $10$ identical pens,of which $4$ are red and $6$ are blue. $3$ pens are taken out at random one after another. Find the probability that all $3$ are blue.

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