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
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
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 ÷ 2 = 21(20)/2 = 210
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