In a league, there are 8 teams. Every team plays exactly two matches against every other team. How many matches are played in the league in all?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 56
Each pair of teams is a selection of 2 teams out of 8, \(^8C_2\). Every pair plays two matches, so the number of pairs is doubled.
Pairs of teams \(\displaystyle =\,^8C_2=\frac{8\times7}{2}=28\)
Matches \(=2\times28=56\)
Why the other options are incorrect
Option (1) 28 — Incorrect. This is the count if every pair played only once.
Option (2) 64 — Incorrect. This is \(8\times8\), which pairs a team with itself as well; a team does not play itself.
Option (3) 112 — Incorrect. This is \(4\times28\); each pair plays 2 matches, not 4.