It looks like your message got cut off! You mentioned a Christmas party where everyone shook hands with everyone else, and you started to mention a total number, but it’s incomplete. If you want to find out, for example, how many handshakes there were at the party, I can help with that!
Handshake Problem Explanation
If there are n people at the party, and everyone shakes hands with everyone else exactly once, the total number of handshakes is given by the formula:
Total handshakes=n×(n−1)2\text{Total handshakes}=\frac{n\times (n-1)}{2}Total handshakes=2n×(n−1)
This is because each person shakes hands with n−1n-1n−1 others, but counting this for all nnn people counts each handshake twice.
Example
If there were 10 people at the party:
Total handshakes=10×92=45\text{Total handshakes}=\frac{10\times 9}{2}=45Total handshakes=210×9=45
If you provide the total number of people or the total handshakes, I can help you solve the problem completely!
