Are You a Fan of Dancing?

Logic Level 4

In a dancing night, there are 120 people including men and women participating (A person can dance to many). A group of three is called a "perfect three" if they dance to each other. After the night, it is said that for each 4 people there exists at least 1 "perfect three". How many pairs are there that have danced (at least)?

Note: The image is from the Visual Novel 'Rewrite'.

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