Solve the Problem $n$ People, the Number of Possible Handshakes $N$ , Is Given By

Multiple Choice

Solve the problem.
-Within a group of $n$ people, the number of possible handshakes, $N$ , is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$ . At a party, everybody shakes hands with every other person. If the total number of handshakes is 253 , how many people are at the party?

A) 24
B) 22
C) 25
D) 23