+33 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?
+2668 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.
