Question:
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____________.
Solution:
Select any 4 correct questions in ${ }^{6} C_{4}$ ways.
Number of ways of answering wrong question $=3$
$\therefore$ Required number of ways $={ }^{6} C_{4}(1)^{4} \times 3^{2}=135$.