A teacher has made ten statements for a True-False test. Four statements are true and six are false. However, no two true statements are consecutive. How many distinct answer keys could there be for the test?
+36916 FOUR ways to keep the four TRUES separated in the line up of 10 questions
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T T T T This is one way.....then you can shift the line of trues to the right 3 more times total 4 ways
+526 Since the only condition is that no 2 trues are consecutive aren't there more than 4 ways to arrange them?
+36916 You are correct.....
they could be separated like this :
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T T T T
or other ways..... let me think about how to derive the answer for a little while......If I come up with a solution I will let ya know !
THANX ! ~ EP
