SOLUTION: Ten new friends shake hands with each other once and once only. How many total number of handshakes would there be?

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Question 1069630: Ten new friends shake hands with each other once and once only. How many total number of handshakes would there be?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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%2810%2A9%29%2F2 = 45.

Each of 10 friends handshakes with each and all other 9 friends,

and for each two pairs (a,b) and (b,a) we register only ONE handshake.

Therefore, we multiply 10 by 9 and then divide by 2.


The outcome is the same as the number of combinations of 10 items taken 2 at a time.