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There were 36 participants in a party, some of whom shook hands with each other, such that any two participants shook hands with each other at most once. Each participant then recorded the number of handshakes made, and it was found that no two participants with the same number of handshakes made had shaken hands with each other. Find the maximum total number of handshakes in the party. (When two participants shook hand with each other this will be counted as one handshake.)

Respuesta :

Answer: There are 630 handshakes at maximum.

Step-by-step explanation:

Since we have given that

Number of participants in a party = 36

We need to find the number of handshakes.

So, By "handshake lemma":

We get the number of shakes that would be

[tex]\dfrac{n(n-1)}{2}\\\\=\dfrac{36(36-1)}{2}\\\\=\dfrac{36\times 35}{2}\\\\=18\times 35\\\\=630[/tex]

Hence, there are 630 handshakes at maximum.

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