Out of 5 girls and 3 boys,4 children are to b | vedclass

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(A) Total number of children $= 5 + 3 = 8$.Number of ways to select $4$ children out of $8$ is given by the combination formula ${}^{n}C_{r} = \frac{n

Vedclass · Accepted Answer

$\frac{1}{14}$

Vedclass · Answer

(A) Total number of children $= 5 + 3 = 8$.Number of ways to select $4$ children out of $8$ is given by the combination formula ${}^{n}C_{r} = \frac{n!}{r!(n-r)!}$.Total ways $= {}^{8}C_{4} = \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 70$.Number of ways to select $4$ girls out of $5$ is ${}^{5}C_{4} = {}^{5}C_{1} = 5$.Probability of selecting $4$ girls $= \frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{5}{70} = \frac{1}{14}$.

Out of $5$ girls and $3$ boys,$4$ children are to be randomly selected for a quiz contest. What is the probability that all the selected children are girls?

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