How many ways can someone answer a test with 10 questions, where the first 2 are false, OR the last 3 questions are true.

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- Nov 16th 2009, 03:23 PMtyrone92True/False questions on a TEST
How many ways can someone answer a test with 10 questions, where the first 2 are false, OR the last 3 questions are true.

- Nov 17th 2009, 01:31 AMGrandad
Hello tyrone92I don't understand the question.

I take it there are $\displaystyle 10$ questions that have either true or false answers. Since each question can be answered in either of $\displaystyle 2$ ways, the number of different ways of answering all $\displaystyle 10$ is $\displaystyle 2^{10}=1024$.

What do you mean 'the first $\displaystyle 2$ are false'? Do we know those answers to be false and have to find combinations of true/false answers to the other $\displaystyle 8$? (In which case there are $\displaystyle 2^8=256 $ possibilities.)

Can you clarify the question please?

Grandad