There are 10 players in a chess group, and each player plays each of t

The total number of games played is 10C2 = (10 x 9)/2! = 45.

Answer: C

this is how I approach this kind of problems as I struggle to apply combinatorics concept on that. I usually draw a table similar to the ones we used in our schoold tournaments. Please see the pic attached:

1. there are 10 players
2. each cross-section stands for the H2H game
3. grey depicts that we cannot play against ourselves (i.e. 1 vs. 1 and etc)
4. as long as we play only once the number of the below yellow squares is the total number of games. Otherwise if we were to play twice (home-away) the area on the other side of the grey row would also become yellow and thus the total number of games would 2x

5. mathematically this looks the following:

10*10 however since we do not play against each other this should be rather 10*9 = 90 games if we played twice. 90/2 = 45 - we face each other once.