Counting Probablity word problem

Lance's math quiz has eight true-false questions. How many different choices for giving answers to the eight questions are possible.

ok I know that if he got all True its 8 and half true half false its 8 all false is 8. So do I just multiply them all or add them? Did I think it through right?

karliekay said:

Lance's math quiz has eight true-false questions. How many different choices for giving answers to the eight questions are possible.

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The answer is \(\displaystyle 2^8\).
Now, please tell us why that is true.

ok why is that the answer.

karliekay said:

ok why is that the answer.

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You may want to review the Fundamental Counting Principle. Here's ONE website that may help you (and there are many others):

http://www.basic-mathematics.com/fundam ... ciple.html

See if, after reading that, you can apply it to your situation where you have 8 tasks to do (answer 8 questions) and each task can be done in two different ways (give an answer of True, or give an answer of False).

I tried doing 2*8 when I first worked the problem and the answer is not 16.

karliekay said:

I tried doing 2*8 when I first worked the problem and the answer is not 16.

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Let's suppose there are only THREE questions on the true-false test.

Ways to answer first question: 2
Ways to answer second question: 2
Ways to answer third question: 2

By the fundamental counting principle, if the first task can be done in "m" ways and the second can be done in "n" ways, then together, the two tasks can be done in m*n ways.

We have three tasks. The first can be done in 2 ways. The second can be done in 2 ways. The third can be done in 2 ways. Together, the three tasks can be done in 2*2*2 ways. 2*2*2 can be written as 2[sup:2r5aqbzk]3[/sup:2r5aqbzk]. And that's not 6.

Thus, 2*8, which gives 16, is not the way to complete your problem.