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lovesuit
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There are 10 teams playing in the football tournament. 14 Oct 2023, 02:34
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45% (medium)

Question Stats:

66% (02:04) correct 34% (01:51) wrong based on 284 sessions

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There are 10 teams playing in the football tournament. Each team plays 27 matches (each team plays 3 matches against the same team). There are 5 playoff matches including the final match. What is the total number of matches played in the tournament?

(A) 275
(B) 248
(C) 167
(D) 140
(E) 113
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D
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Nsingh06
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There are 10 teams playing in the football tournament. 14 Oct 2023, 04:34
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Can someone please share the solution for this?

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Bunuel
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There are 10 teams playing in the football tournament. 14 Oct 2023, 06:18
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lovesuit
There are 10 teams playing in the football tournament. Each team plays 27 matches (each team plays 3 matches against the same team). There are 5 playoff matches including the final match. What is the total number of matches played in the tournament?

(A) 275
(B) 248
(C) 167
(D) 140
(E) 113
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The number of pairs possible from 10 teams is 10C2 = 10!/(8!2!) = 45. Each pair plays 3 games; hence, we get 45*3 = 135 games. Adding 5 playoff games gives a total of 140 games.

Answer: D.
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There are 10 teams playing in the football tournament. 13 Jan 2026, 22:51
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27*10 = 270 matches but we counted double thats why 270/2=135 total matches + 5 extra = 140
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There are 10 teams playing in the football tournament. 15 Jan 2026, 15:27
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Deconstructing the Question
Total Teams = 10.
Matches per team in league stage = 27.
Playoff matches = 5.

Target: Total number of matches.

Step 1: Calculate League Matches
If we sum the matches played by each team individually:
\(\text{Sum} = 10 \text{ teams} \times 27 \text{ matches/team} = 270\).

Since every match involves 2 teams, the above sum counts each match twice.
\(\text{Actual League Matches} = \frac{270}{2} = 135\).

Alternative approach:
Number of unique pairs of teams = \(^{10}C_2 = \frac{10 \times 9}{2} = 45\).
Each pair plays 3 times.
Total = \(45 \times 3 = 135\).

Step 2: Add Playoff Matches
Total Matches = League Matches + Playoff Matches
Total Matches = \(135 + 5\)
Total Matches = \(140\).

Answer: (D)
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