It's party time

Probability Level 2

Alice invites six guests to her birthday party: Bob, Carl, Diane, Eve, Frank, and George. When they arrive, they shake hands with each other (strange European custom). This group is strange, because one of them asks, “How many handshakes are there in total?"

What is the answer to the question above?


The answer is 21.

Abhishek Alva by abhishek alva , 19, India

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3 solutions

There are 7 people and a handshake requires two people. Which implies that the no. of handshakes = 7C2 = 7 X 6 2 \frac{7X6}{2} .=21

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No. of handshakes = ( n 2 ) ( n − 1 ) = ( 6 ) ( 7 ) / 2 = 21 (\frac{n}{2})(n-1)=(6)(7)/2=21

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Abhishek Alva
Dec 27, 2016

there are 7 people .let us rename them as a, b, c ,d , e, f, g .now if a can shake hands with the other 6 .now b can shake hands with the remaining 5 (b has already shaken hands with a ) and so on .so it is 6+5+4+3+2+1=21

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