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?

This is the same as counting the number of identifiable"words" that can be formed with four "T's" and six "F's"

So

[ Total Letters ! ] / [ Repeats of T ! x Repeats of F ! ] =

10! / [ 4! * 6! [ =

210 distinct answer keys