How many different answer sheets can be submitted?

Question

For this problem, assume the test had 7 true-false questions and 7 multiple-choice questions, and that each multiple-choice question had 5 choices.

Answer 1

There are 7 T/F questions.  Each of these has 2 possible answers, so there are 2⁷ different combinations of answers to these questions.

 

There are 7 multiple-choice questions, and each of these has 5 possible answers, so there are 5⁷ different combinations of answers to these questions.

 

So there are 2⁷5⁷ = 10⁷ = 10,000,000 different possible answer sheets.

 

HOWEVER...  It's possible, isn't it, that someone could leave an answer blank.  In a sense, that counts as one more possible answer for each question.  So that would mean there are 3 possible answers to each T/F question and 6 possible answers to the multiple-choice.  So that means there are 3⁷6⁷ possible answer sheets when you allow for blanks.  That's 612,220,032.