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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
avatar+33 
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Never mind I got it 

 

Thanks though

 Jan 27, 2023
 #2
avatar+2667 
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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
avatar+33 
+1

Thank you BuilderBoi

 Jan 27, 2023

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