Question 1
An election is held among 21 candidates. What is the total number of pairwise comparisons in this election?
◦ 21
◦
![](data:image/png;base64, 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)
◦ 21
2◦ 21 × 2
◦ 2
21Question 2
In a round robin tennis tournament, every player plays against every other player. If 11 players are entered in a round robin tennis tournament, how many matches will be played?
◦
![](data:image/png;base64, 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)
◦ 11 × 2
◦ 2
11◦ 11
2◦ 11 × 10