Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible ?
A)440
B) 1,280,000
C) 3,072
D) 40,960
E) 2,097,152

Question

Professor Tough's final examination has 11 true/false questions followed by 5 multiple choice questions. In each of the multiple choice questions you must select the correct answer from a list of 4. How many answer sheets are possible  ?
A)440
B) 1,280,000
C) 3,072
D) 40,960
E) 2,097,152

Quizplus · Accepted Answer

For the true/false questions, there are 2 possibilities for each question, making it $2^{11}$ possibilities. For the multiple choice questions, there are 4 possibilities for each question, making it $4^5$ possibilities. The total number of possible answer sheets is the product of these two, which is $2^{11} \times 4^5 = 2,048 \times 1,024 = 2,097,152$.

Professor Tough's Final Examination Has 11 True/false Questions Followed by 5