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 ${=}^6{\mathrm{C}}_4$
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

$\begin{array}{l}{=}^6{\mathrm{C}}_4\times 1\times 9\\ =\frac{6!}{2!4!}\times 9\\ =\frac{6\times 5}{2}\times 9=135\end{array}$