Question

in a round robin tennis tournament involving 7 players, each player will play every other player twice. How many total matches will be played in the tournament?

Answer 1

Total number of ways to make a pair:

The first player can be any one of 7 .  For each of those . . .
The opponent can be any one of the remaining 6 .

Total ways to make a pair  =  7 x 6 = 42 ways .

BUT ... every pair can be made in two ways ...  A vs B  or  B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.

If every pair plays 2 matches, then  (21 x 2) = 42 total matches will be played.


Now, is that an elegant solution or what !