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

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

math  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

math  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.

math  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 รท 2 = 21(20)/2 = 210
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