Posted by **mark** on Sunday, February 10, 2013 at 8:06pm.

taylor was having a party.she invited 20 friends to her party, if each person shook hands with every other person .how many handshakes would there be? please explain,thanks

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**Ms. Sue**, Sunday, February 10, 2013 at 8:09pm
21 * 20 = ?

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**Reiny**, Sunday, February 10, 2013 at 9:38pm
Each of the 20 people will shake hands with 19 other people

20(19)= 380

but that would include duplicates such as A shaking hands with P, and P shaking hands with A, which is the same handshake

so number of handshakes = 20(19)/2 = 380/2 = 190

or

we are choosing pairs from 20

= C(20,2) = 190

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**Ms. Sue**, Sunday, February 10, 2013 at 9:40pm
Thanks, Reiny -- I goofed and didn't consider that we can't count A and P and P and A.

I included the hostess -- so we have 21 people.

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**Reiny**, Sunday, February 10, 2013 at 10:11pm
Thanks Ms Sue, and I didn't catch the hostess part, only saw the 20.

So let's go with your answer ÷ 2 = 21(20)/2 = 210

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