2017 AMC 10A Problems/Problem 8

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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. ! Undefined control sequence.)

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