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.

Click here to see ALL problems on Miscellaneous Word Problems

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
------------
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.
-----------
Cheers,
Stan H.