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How do I solve the following combinations problem?The sociology test has 15 true/false...

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catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted August 17, 2011 at 2:07 PM via web

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How do I solve the following combinations problem?

The sociology test has 15 true/false questions. In how many ways can you answer 11 correctly?

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted August 17, 2011 at 2:41 PM (Answer #1)

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A combination is when there is no repetition and order doesn't matter.  The theorem is...

n! / r!(n-r)!

where n is the number of things to choose from (in this case true/false questions) and you choose r of them (in this case the questions that are answered correctly.

n = 15

r = 11

15! / 11!(15-11)!

15! / 11! * 4! = 1365

There are 1365 ways to answer 11 correctly.

 

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