An exam consists of nine true-or-false questions. Assuming that every question is answered, in how many different ways can a student complete the exam? In how many ways may the exam be completed if a penalty is imposed for each incorrect answer, so that a student may leave some questions unanswered?
A) 129; 587
B) 146; 7,159
C) 512; 19,683
D) 637; 38,777
E) 161; 11,858
F) 587; 14,685

Question

An exam consists of nine true-or-false questions. Assuming that every question is answered, in how many different ways can a student complete the exam? In how many ways may the exam be completed if a penalty is imposed for each incorrect answer, so that a student may leave some questions unanswered? ​
A) 129; 587
B) 146; 7,159
C) 512; 19,683
D) 637; 38,777
E) 161; 11,858
F) 587; 14,685

Quizplus · Accepted Answer

For each question, there are 2 choices (true or false), so there are $2^9 = 512$ ways to answer all the questions.
If there is a penalty for incorrect answers, there are 3 choices for each question (true, false, or leave unanswered), so there are $3^9 = 19,683$ ways to answer the exam.

An Exam Consists of Nine True-Or-False Questions