In each question, we have two options True and False.
There are 6 questions.
We have 2 options for the first question, two options for the second question, two options for the third question, ...
We got
[tex]2\times2\times2\times2\times2\times2=2^6[/tex][tex]=64[/tex]Hence there are 64 ways to answer a six-question true-false quiz.
In general for n questions we get
[tex]2^n\text{ ways }[/tex]