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In a tennis tournament, each of eight players will play three sets aga

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Carcass
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In a tennis tournament, each of eight players will play three sets aga [#permalink] New post   22 Nov 2021, 08:37
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In a tennis tournament, each of eight players will play three sets against each other player. How many sets will be played in total?

A) 28

B) 64

C) 84

D) 128

E) 168
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C
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Niraj137
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Re: In a tennis tournament, each of eight players will play three sets aga [#permalink] New post   22 Nov 2021, 08:55
Number of pairs of two that can be formed by 8 players = \(^8C_2 = \frac{8*7}{2*1} = 4*7 = 28\)

Each pair of players play 3 matches.

Therefore, total number of matches = \(28*3 = \textbf{84}\)

Hence, Answer is C
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Re: In a tennis tournament, each of eight players will play three sets aga [#permalink] New post   22 Nov 2021, 09:34
Carcass wrote:
In a tennis tournament, each of eight players will play three sets against each other player. How many sets will be played in total?

A) 28

B) 64

C) 84

D) 128

E) 168

Let the 8 players by A, B, C, D, E, F, G, and H

Each player will play against 7 players, and each game consists of 3 sets.
(7)(3) = 21, so each player will play 21 games

There are 8 players, so the total number of games played = (8)(21) = 168

HOWEVER, before we select answer choice E, we must recognize that every set played has been counted TWICE.
For example, players B and G play 3 sets against each other. Player B counted those 3 sets, and player G also counted the same 3 sets.

To account for this duplication, we must divide 168 by 2 to get: 84

Answer: C
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Re: In a tennis tournament, each of eight players will play three sets aga [#permalink]
22 Nov 2021, 09:34
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