At the first meeting of the Table Tennis Club, the seven members decide to have a tournament in which each player will play a game against each other player. How many games will there be?

Question

anonymous · Answer

i got 49

but i think thats wrong

anonymous · Answer

This is number of combinations of 7 things taken 2 at a time
n!/r!(n-r)! = 7! / 2! (5!) = 7 * 6 / 2 = 21

Label players A to G
A plays B to G:   6 games
B plays C to G:   5 games
C plays D to G:   4 games
D plays E to G:    3 games
E plays F to G      2 games
F plays G:            1 game

total: 21 games      nice when it works out as it should!

anonymous · Answer

Good night!