Question

567 teams participate in a football tournament. If each team plays against every other team only once how many matches will be played in total

Answer 1

Given:

567 teams in a football tournament and each team play each other once.

To find:

The total number of matches played.

Solution:

We will solve the given condition by combination:

• The total number of teams = 567
• The total number of teams per match = 2

Now,

we will apply the combination;

ⁿCₐ = n!/r!(n-r)!

where

n = 567

a = 2

• ⁵⁶⁷C₂ = 567!/2!(567-2)!
• ⁵⁶⁷C₂ = 567!/2!565!
• ⁵⁶⁷C₂ = 567×566×565!/2!565!
• ⁵⁶⁷C₂ = 567×566/2×1
• ⁵⁶⁷C₂ = 567×283
• ⁵⁶⁷C₂ = 160461

so, the total number of matches played is 160461