Handshake

Probability Level 2

If you are at a party with 17 other people and everyone shakes hands with everyone else exactly once, how many handshakes have been made?


The answer is 153.

Ibrahim Said by Ibrahim Said , 25, Egypt

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2 solutions

Elmer Rodriguez
May 22, 2020

One needs to read the question carefully.There are 18 people involved so 18C2=153.

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Kay Xspre
Oct 14, 2015

You have a total of 18 people, and each of them shake hand with each other once (except yourself), it will satisfy 18 C 2 = 18 ! 16 ! 2 ! = 17 × 18 2 = 153 ^{18}C_2\ = \frac{18!}{16!2!} = \frac{17\times18}{2} = 153

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