If there are twenty people sitting around a table, how many different combinations of two people can have conversations during dinner ?

Question

HS Geometry

Answer 1

Hi Emma.  I think the formula is n!/k!(n-k)!

 

I think that would be 20!/2!(20-2)!  = 20!/2!(18)! = 20 x 19/2 x 1 = 380/2 = 190.

 

I haven't done one of these in 45 + years... You better check with someone...

Answer 2

I believe the answer is still ₂₀C₂ = 190, i.e. the number of groups of 2 selected from 20.  This assumes that people can have a conversation across the table.

 

However, the answer will be different if what is being asked is limited to couples sitting next to each other, in which case I think the answer is 20.