An exam consits of three true/false questions followed by five multiple choice questions each with 3 answers.
How many ways can a student answer the exam if they can leave any of the questions blanks?

Question

An exam consits of three true/false questions followed by five multiple choice questions each with 3 answers.
How many ways can a student answer the exam if they can leave any of the questions blanks?

anonymous · Answer

They have 3 choices: true, false, and blank.
And they have 3 questions where order matters.

so it's just $$ 3^3 = 27$$

anonymous · Answer

Hmm I think there is a lot more ways then just 27 if that is what you're saying.

anonymous · Answer

oops  you're right, I just solved for the multiple choice section
give me a second

anonymous · Answer

So for multiple choice, you have 4 answers, 3 normal answers and 1 for blank.

So it's:
$$4^5=1024$$

while for the first part of the test its:
$$3^3=27 $$

We multiply them, because when you must do two tasks in sequence you multiply
(When you do two tasks in parallel you add)

from before and we get 
$$ 27648 $$

anonymous · Answer

sorry for my misunderstanding

anonymous · Answer

Oooooh! No, I totally get it. I never considered blank being an option. Wow that is so much easier then trying to figure out which spots are blank at which outcomes. Haha thank you