Discussion
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches?
Answer: B
The league needs 10 matches.
Each match is a pair of teams, and every pair plays exactly once, so the number of matches is the number of ways to choose 2 teams from 5:
\[ \binom{5}{2} = \frac{5 \times 4}{2} = 10 \]
20 counts each match twice, once from each team's point of view (5 teams \(\times\) 4 opponents). 5 and 8 do not come from any correct count.
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