five friends are having a tennis tournament .each friend will play the other four friends once.how many matches will be played
English · Middle School · Tue Nov 03 2020
Answered on
Given:
Five friends having a tennis tournament
Each friend will play with the other four friends once.
Determine how many matches will be played in total.
Solution:
The easiest way to approach this problem is to schedule the games for each friend. Let A, B, C, D, and E, represent the five friends who will be competing. We'll start by having player A play everyone in a row. After player A has played everyone. We'll then move on to the remaining games for B and so on.
A-plays the other 4 friends in 4 games so no one has to play A after that.
(A vs B)
(A vs C)
(A vs D)
(A vs E)
Total Games: 4
B-plays the remaining 3 friends.
(B vs C)
(B vs D)
(B vs E)
Total Games: 3
C-plays the remaining 2 friends.
(C vs D)
(C vs E)
Total Games: 2
Lastly D-plays E.
(D vs E)
Total Game: 1
Add up the games
4+3+2+1=10
Final Answer: 10 games played