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

Out of 6 questions, four questions can be chosen in ${ }^6{C}_4$ways. Each of these four selected questions can be answered correctly in exactly one way and each of the remaining 2 questions can be answered wrongly in 3 ways. So, required number of ways is ${ }^6{C}_4\times 1^4\times 3^2=135$.