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At a gathering of \(30\) people, there are \(20\) people who all know each other and \(10\) people who know no one.

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At a gathering of \(30\) people, there are \(20\) people who all know each other and \(10\) people who know no one.

by BTGmoderatorLU » Fri Dec 01, 2023 9:29 am

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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 within the group?

A. \(240\)
B. \(245\)
C. \(290\)
D. \(480\)
E. \(490\)

The OA is B
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Re: At a gathering of \(30\) people, there are \(20\) people who all know each other and \(10\) people who know no one.

by adamarkin » Sun Dec 17, 2023 8:46 pm
For the 10 people who know no one, there are (C(10, 2) = \frac{10 \times 9}{2} = 45) handshakes.

For the 20 people who all know each other, there are no handshakes as they all hug.

Adding both, the total number of handshakes is (45).
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