SOLUTION: If there are 20 people in a room, and each person shakes hands with everyone exactly once, how many handshakes will there be? Thanks for the help.

Question 127037: If there are 20 people in a room, and each person shakes hands with everyone exactly once, how many handshakes will there be?
Thanks for the help.
Found 3 solutions by scott8148, checkley71, stanbon:
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
each of the 20 people shakes hands with 19 other people __ 20*19=380

BUT ... Sam shaking hands with Sue is the same as Sue shaking hands with Sam
__ so half of the handshakes are duplicates

(20*19)/2=190
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1=190 hand shakes.
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
19C2 = 19*18/1*2 = 19*9 = 171
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You can see this pattern if you try it with
2 people = 2C2 = 1 handshake
3 people = 3C2 = 3 handshakes
4 people = 4C2 = 6 handshakes
5 people = 5C2 = 10handshakes
etc.
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Cheers,
Stan H.
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