In a multiple-choice test consisting of 8 que | vedclass

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(D) The total number of questions is $n = 8$. Each question has $4$ options,meaning there is $1$ correct option and $3$ incorrect options. The student

Vedclass · Accepted Answer

$1512$

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(D) The total number of questions is $n = 8$. Each question has $4$ options,meaning there is $1$ correct option and $3$ incorrect options. The student needs to choose exactly $5$ correct answers out of $8$. The number of ways to select $5$ questions to be correct is given by the combination formula $\binom{8}{5}$. For the $5$ correct questions,there is only $1$ way to choose the correct option. For the remaining $8 - 5 = 3$ incorrect questions,each can be answered in $3$ different ways (since there are $4$ options and $1$ is correct,$4 - 1 = 3$ are incorrect). Thus,the total number of ways is $\binom{8}{5} 	imes (1)^5 	imes (3)^3$. Calculating this: $\binom{8}{5} = \binom{8}{3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$. Total ways $= 56 	imes 1 	imes 27 = 1512$.

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