unfortunately, i went the long way. it took about 2:20 to do.

since there are 20 teams, and each team plays the other team a total of 10 times, then the 1st team will play a total of 190 games (there are 19 other teams played 10 times each so 19*10 = 190), our second team will play a total of 180 games, our 3rd team will play 170.......
adding all of these up, we get 1800.

hopefully someone can post an answer that is shorter. i'm not the best with combination-type problems.

Master Bunuel might be able to provide a good explanation.

It should be 1900

1st team:190
2nd team:180
3rd team :170

Similarly the last team will play 0

therefore(190+180+170....10)

10(19+18+17+16....1)

10 (n(n+1)/2)=10(19*20/2)=1900

Each possible pairing of 20 teams plays 10 times
There are C(20,2) pairings

So no of matches = C(20,2) * 10 = 190 * 10 = 1900
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Choose 2 teams out of 20 teams = 20C2 = 190 (sets that can be formed)
Each set of team plays 10 games = 190 * 10 = 1900.

Should be 1900! Can the original poster please clarify the answer again and the source ?
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I remember for such problems we perhaps need to divide the total number of games by 2, as two teams play each other, so isn't that true here, or am I missing something ?

Regards,
Subhash
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Poster said "Kudos for the first who answers with the right answer"
And all provided answers are wrong... where is the poster OMG.

The correct answer is 1900. Edited option A.
Correct solution is here: there-are-in-a-certain-league-20-teams-and-each-team-face-107442.html#p847594

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Thanks Bunuel, You are so fast.

one game with each team ; 20c2 ; 190
so 10 times ; 190*10 ; 1900
IMO A

If each team were to play a game against the rest of the teams, we would have 20 * 19 amount of games in total. However, this results in each team facing each other twice since we counted both A faces B and B faces A. To eliminate the double-counting, we divide that value by 2 to get 10*19 = 190 games played. Finally, we multiply that by 10 to get 1900 games in total for facing each other 10 times instead of once.

Ans: A
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Solution

Given
• In a certain league, there are 20 teams,
• Each team faces another team for a total of 10 times

To find
• The number of games to be played in the season.

Approach and Working out
For one match, there must be two teams.
• So, total match if only one match is played between two teams = 20 c2 = 190.
• However, each team plays 10 matches between them.
o So, total matches in the season = 190*10 = 1900

Hence, option A is the correct answer.

Correct Answer: Option A
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