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# How do I solve this using combination

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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?

Apr 24, 2019

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Formula for picking items from n set: $$\frac{n!}{r!(n-r)!}$$

Since you are trying to find the combinations for a ten question test with 4 true and 6 false, you can just think it as picking 4 items from a set of 10 or picking 6 items from a set of 10.

Note: There are the same amount of combinations picking 4 items from a set of 10 is the same thing as picking 6 items from a set of 10

Now use the formula.

Apr 24, 2019
edited by CalculatorUser  Apr 24, 2019