how do you find out how many people are in the tournament?

Question

you are scheduling a round robin tennis tournament. Each participant will play against every other participant once. how many matches will be played?

Answer 1

x is the number of participants.  The number of matches will equal (x-1)!

1 player  0 matches

2 players (2-1)! = 1!=1

3 players (3-1)!= 2!=2

4 players (4-1) factorial = 3!=3*2*1

 when four players, The first player plays three times, the next player has two other unique matches, the third player has one unique match.

 

You can use dots to represent each player and draw connecting arrows between the dots to show a match.  connect every dot with every other dot and add up the connections.  Adding up the connecting arrows will give us the same answer but using factorials can be done very quickly on a calculator.