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There are 16 teams in a soccer league, and each team plays each of the

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There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 12 Sep 2015, 12:35
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There are 16 teams in a soccer league, and each team plays each of the others once. Given that each game is played by two teams, how many total games will be played?

A. 256
B. 230
C. 196
D. 169
E. 120

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Re: There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 12 Sep 2015, 15:43
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Hi shasadou,

This question can be answered in a couple of different ways. If you know the Combination Formula, then you can use that...

N!/[K!(N-K)!] where N is the total number of Teams and K is the Subgroup.

In this prompt, N = 16 and K = 2...

16!/[2!(14!)] =

(16)(15)/(2)(1) =

120 different games played

You can also use 'brute force' and a bit of logic to answer the question....

Let's call the teams...ABCDE FGHIJ KLMNO P

Team A plays each of the other 15 teams, so that's 15 games.
Team B already played Team A, so it plays 14 OTHER games.
Team C already played Teams A and B, so it plays 13 OTHER games.
Team D already played Teams A, B and C, so it plays 12 OTHER games.
Etc.

The sum of all of these games is...
15+14+13.....+3+2+1 = 120

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There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 12 Sep 2015, 13:51
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shasadou wrote:
There are 16 teams in a soccer league, and each team plays each of the others once. Given that each game is played by two teams, how many total games will be played?

A. 256
B. 230
C. 196
D. 169
E. 120



SIMPLY USE ( N (N-1) )/2 TAKE N = 16 ..

ANSWER E

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Re: There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 06 Aug 2019, 18:38
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16 teams play 15 other teams. 16*15. because there are 2 teams per game, to not double count, divide by 2. 16 *15. This is the same principle as those questions that ask for how many handshakes
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Re: There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 08 Aug 2019, 20:16
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Every team will play with every other team and there are 16 teams.
SO total number of matches = 16.15
But here (16*15), one match is counted twice,
So Ans = 16*15/2 = 120.
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Re: There are 16 teams in a soccer league, and each team plays each of the  [#permalink]

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New post 06 Aug 2019, 21:24
In the question order does not matter
16C2 = 16!/(2!x14!) = 120
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Re: There are 16 teams in a soccer league, and each team plays each of the   [#permalink] 06 Aug 2019, 21:24
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