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?
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
Since the only condition is that no 2 trues are consecutive aren't there more than 4 ways to arrange them?