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# Help with problem

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A teacher has made ten statements for a True-False test. Four statements are true and six are false. How many distinct answer keys could there be for the test?

Jan 27, 2023

#1
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Never mind I got it

Thanks though

Jan 27, 2023
#2
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There are 4 spots for the questions that are true, and the remaining 6 must go for the ones that are false.

There are $${10 \choose 4} = {10! \over 6! \times 4!} = \color{brown}\boxed{210}$$ possible answer keys.

Note that this is the same thing as choosing 6 spots for the questions that are false.

Jan 27, 2023
#3
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Thank you BuilderBoi

Jan 27, 2023