A test consists of $$6$$ multiple choice questions, each haying $$4$$ 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

Question

Infinity Learn · Accepted Answer

Number of ways to select four questions from six questions $=^{6} C_{4}$
And number of ways to answer these questions correctly=1x1x1x1=1
And number of ways to answer remain two questions wrongly = 3 x 3 = 9
Required number of ways

$\begin{array}{l} =^{6} C_{4} \times 1 \times 9 \\ = \frac{6!}{2! 4!} \times 9 \\ = \frac{6 \times 5}{2} \times 9 = 135 \end{array}$

Combinations

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A test consists of 6 multiple choice questions, each haying 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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Combinations

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A test consists of 6 multiple choice questions, each haying 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

Number of ways to select four questions from six questions =6C4And number of ways to answer these questions correctly=1x1x1x1=1And number of ways to answer remain two questions wrongly = 3 x 3 = 9Required number of ways=6C4×1×9=6!2!4!×9=6×52×9=135

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