A test consists of 6 multiple choice question | vedclass

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Question

(A) The total number of questions is $n = 6$.The number of correct answers required is $r = 4$.For each question,there is $1$ correct answer and $3$ i

Vedclass · Accepted Answer

$135$

Vedclass · Answer

(A) The total number of questions is $n = 6$.The number of correct answers required is $r = 4$.For each question,there is $1$ correct answer and $3$ incorrect answers.The number of ways to choose $4$ questions out of $6$ to be correct is given by the combination formula ${}^{6}C_{4}$.For the $4$ correct questions,there is only $1$ way to answer each correctly $(1^4)$.For the remaining $6 - 4 = 2$ questions,each must be answered incorrectly,and there are $3$ choices for each incorrect answer $(3^2)$.Therefore,the total number of ways is ${}^{6}C_{4} 	imes 1^4 	imes 3^2 = 15 	imes 1 	imes 9 = 135$.

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all six questions such that exactly four of the answers are correct is:

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