# Thread: Confused on what to do here..

1. ## Confused 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?

2. Originally Posted by eh501
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?

No. Let A B C D E be the people. Then A shakes hands with B,C,D,E. Then B shakes hands with C,D,E but not A because they already shook hands. Then C shakes hands with D,E. And D shakes hands with only E.

3. How would you know when to do that, when to multiply or when to add?

4. Originally Posted by eh501
How would you know when to do that, when to multiply or when to add?
Each problem is different, you need to understand how to approach a problem and decide whether you have to add or multiply.

You can also do it another way. Draw a picture and the lines represent the people who shook hands. Then count the number of lines.

5. Ok, so whats the answer?

6. Originally Posted by eh501
9. 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 $^n\mathrm{C}_2=\frac{n(n-1)}{2}$.