Five friends met for lunch, and they all shook hands. Each person shook the other persons right hand only once. What was the total number of handshakes?

Would you add 5+5?

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- Jan 23rd 2008, 11:59 AMeh501Confused on what to do here..
Five friends met for lunch, and they all shook hands. Each person shook the other persons right hand only once. What was the total number of handshakes?

Would you add 5+5? - Jan 23rd 2008, 12:32 PMThePerfectHacker
- Jan 23rd 2008, 12:34 PMeh501
How would you know when to do that, when to multiply or when to add?

- Jan 23rd 2008, 12:37 PMThePerfectHacker
- Jan 23rd 2008, 12:42 PMeh501
Ok, so whats the answer?

- Jan 23rd 2008, 12:52 PMThePerfectHacker
- Jan 23rd 2008, 12:55 PMeh501
I know you did but i really don't know what to do..do i just add up the letters? I still came up with 10.

- Jan 23rd 2008, 12:58 PMThePerfectHacker
- Jan 23rd 2008, 02:34 PMJaneBennet
If

*n*people shake hands with each other such each pair of persons shake hands once and only once, the total number of handshakes is $\displaystyle ^n\mathrm{C}_2=\frac{n(n-1)}{2}$.