A student has to answer a multiple-choice que | vedclass

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Question

(D) The total number of ways to select any number of alternatives from $5$ available alternatives is given by the sum of combinations: $\binom{5}{0} +

Vedclass · Accepted Answer

$26$

Vedclass · Answer

(D) The total number of ways to select any number of alternatives from $5$ available alternatives is given by the sum of combinations: $\binom{5}{0} + \binom{5}{1} + \binom{5}{2} + \binom{5}{3} + \binom{5}{4} + \binom{5}{5} = 2^5 = 32$. Since the student must choose two or more than two alternatives,we must exclude the cases where $0$ or $1$ alternative is chosen. The number of ways to choose $0$ alternatives is $\binom{5}{0} = 1$. The number of ways to choose $1$ alternative is $\binom{5}{1} = 5$. Therefore,the number of ways to choose two or more alternatives is $32 - (1 + 5) = 32 - 6 = 26$.

$A$ student has to answer a multiple-choice question having $5$ alternatives in which two or more than two alternatives are correct. Then the number of ways in which the student can answer that question is

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