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: 135
Solutions · 1
Official solution
Choose which 4 of the 6 questions are answered correctly: (46)=15. The other 2 questions must be answered incorrectly: 3 wrong choices each: 32=9.
\[\text{Total} = 15\times9 = 135\]