Sixteen players participate in a table tennis tournament. If the organisers adopt a round robin method,what will be the total possible number of tournament matc

Question

Sixteen players participate in a table tennis tournament. If the organisers adopt a round robin method,what will be the total possible number of tournament matches played

Answer 1

2 players --> 1 match = ₂C₂

3 players --> 3 matches = ₃C₂

4 players --> 6 matches = ₄C₂

5 players --> 10 matches = ₅C₂

For n players, we need _nC₂ matches. This makes sense, as its the same as the number of unique ways to select two people from n people, where order of selection does not matter.

Plugging in n=16: ₁₆C₂ = 16! / ((14!)(2!)) = 16*15 / 2 = 120