In a tournament there are 10 teams. Every team plays exactly two matches against every other team. How many matches are played in the tournament in all?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 90
Each pair of teams is a selection of 2, \(^nC_2\), and every pair plays two matches, so the count of pairs is doubled.
Pairs of teams \(\displaystyle =\,^{10}C_2=\frac{10\times9}{2}=45\)
Matches \(=2\times45=90\)
Why the other options are incorrect
Option (1) 45 — Incorrect. This counts only one match for each pair of teams.
Option (2) 100 — Incorrect. This is \(10\times10\), which even pairs a team with itself.
Option (4) 180 — Incorrect. This is \(4\times45\), four matches per pair instead of two.