AHSME 1951 Problem 31

A total of $28$ handshakes were exchanged at the conclusion of a party. Assuming that each participant was equally polite toward all the others, the number of people present was: $\textbf{(A)}\ 14 \textbf{(B)}\ 28 \textbf{(C)}\ 56 \textbf{(D)}\ 8 \textbf{(E)}\ 7$