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How do I solve the following combinations problem?Seven people are applying for two...

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

Posted August 17, 2011 at 2:08 PM via web

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How do I solve the following combinations problem?

Seven people are applying for two vacant school board positions; four are women, three are men. In how many ways can these vacancies be filled

1. With any two applicants?

2. With ony women?

3. With one man and one woman?

 

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

Posted August 17, 2011 at 2:49 PM (Answer #1)

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A combination has no repetition and the order does not matter.  The theorem is...

n! / r!(n-r)!

where n is the number of things to choose from and you choose r of them.

n = 7 applicants

r = 2 vacancies

7! / 2!(7-2)! = 21 ways

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