2017 AMC 10A Problems/Problem 8

Problem

At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other a hug, and people who do not know each other shake hands. How many handshakes occur?

$\textbf{(A)}\240\qquad\textbf{(B)}\245\qquad\textbf{(C)}\290\qquad\textbf{(D)}\480\qquad\textbf{(E)}\490$ (Error compiling LaTeX. Unknown error_msg)