Question

Professor Easy's final examination has 13 true-false questions followed by 2 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of four. How many answer sheets are possible?

My Work:
A) 13x2=26
B) 2x4=8
C) 8+26=32

Answer 1

131,072 possible answers

Explanation:

For the true-false questions, there are only 2 possible outcomes for each question, since the exam has 13 questions, the number of possible answer sheets for this section of the test is:

`T = 2*2*2*2... = 2^(13)`

For the multiple-choice questions, there are two questions with four possible outcomes. The number of possible answer sheets for this section of the test is:

`M = 4*4= 4^2`

Therefore, the number of possible answer sheets (A) for the entire test is given by:

`A= T*M\\A= 2^(13)*4^2\\A=131,072`