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

Answer 1

Ways of selecting correct questions
$={}^6{C}_4=15$
Ways of doing them correct $=1$
Ways of doing remaining 2 questions incorrect $=3^2=9$
$\therefore$ The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct
$=15\times 1\times 9=135$