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Gathering Handshake Counting

1150BeginnerGraph TheoryCombinatorics

AMC 10A · 2017 · Problem 8

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 hug, and people who do not know each other shake hands. How many handshakes occur?

Answer choices

A
240
B
245
C
290
D
480
E
490
0 students attempted0% solvedRating 1150

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