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If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?  

 Aug 31, 2023
 #1
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Seven people must shake hands with six other people.... you might think that is 42 handshakes ....BUT...each handshake involves TWO people so the total number of handshakes is 1/2 of 42 = 21 handshakes. 

 Sep 1, 2023
 #2
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Nice work. 

history  Sep 4, 2023
edited by history  Sep 4, 2023
 #2
avatar+753 
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Correct!

history  Sep 4, 2023
 #3
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To find the number of handshakes, we can use the formula for the sum of the first n-1 positive integers, which is given by (n-1)n/2. 

In this problem, n is equal to seven since there are seven people. 

Using the formula, the number of handshakes will be (7-1) * 7/2 = 6 * 7/2 = 42/2 = 21. 

Therefore, there will be 21 handshakes in total.

 Sep 8, 2023

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