Posted by **donna** on Thursday, April 22, 2010 at 10:56pm.

At a party, there were 105 handshakes. If each person shook hands exactly once with every other person, how many people were at the party?

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**Reiny**, Thursday, April 22, 2010 at 11:00pm
for n people there will be C(n,2) handshakes

C(n,2) = 105

n!/(2!(n-2)!) = 105

n(n-1)/2 = 105

n^2 - n - 210 = 0

(n-15(n+14) = 0

n = 15 or n=-14, but n > 0

so there were 15 people

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