6 seats at the table and there are 24 people. what is the mathematic formula to create as many meetings as long as everyone met other people

Question

i need a formula to create a table where everyone meet each other out of 24 people group as many as everyone met each other

Answer 1

Perhaps this is like the traditional problem of how many handshakes are required between n people so that every individual has shaken hands with every other person, exactly once.

That answer is, in this case, ₂₄C₂ = 276.

 

Dividing this into groups of 6 to sit at the table, I got 46 as the quotient--46 different seatings to accomplish all possible meetings (a.k.a. handshakes).