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# There are 8 teams in a certain league and each team plays each of the

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Joined: 09 Mar 2016
Posts: 1221
Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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25 Dec 2017, 13:22
Bunuel wrote:
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is $$C^2_{8}=28$$.

P.S. Please read and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention ot the points #3 and #8.

Bunuel lets say teams are as follows: A, B, C, D, E, F, G, H. So by using the simple combinatorics formula how do we exclude repeated teams ? I mean if A played with B - this is one game, and it could be also B WITH A ? yeah sounds a bit silly but how do we exclude such repetition thanks!
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Joined: 02 Sep 2009
Posts: 61414
Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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25 Dec 2017, 20:07
dave13 wrote:
Bunuel wrote:
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is $$C^2_{8}=28$$.

P.S. Please read and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention ot the points #3 and #8.

Bunuel lets say teams are as follows: A, B, C, D, E, F, G, H. So by using the simple combinatorics formula how do we exclude repeated teams ? I mean if A played with B - this is one game, and it could be also B WITH A ? yeah sounds a bit silly but how do we exclude such repetition thanks!

8C2 gives the number of different unordered pairs possible from 8:
(A, B)
(A, C)
...
(B, H)
...
(G, H)

So, (A, B) is there only once (there is no (B, A) there)

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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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18 Mar 2018, 07:12
Bunuel wrote:
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is $$C^2_{8}=28$$.

P.S. Please read and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention ot the points #3 and #8.

Bunuel you know I got confused by your shortcut solution until figured out all possible combinations in details . you know what surprises how this expression $$C^2_{8}=28$$
excludes the possibility of playing more than one game by two distinct teams, also it exludes repeated games like AB and BA....

let 8 teams be A, B, C, D, E, F, G, H

NUMBER OF GAMES PLAYES BY TWO TEAMS AS FOLLOWS:

AB BC CD DE EF
AC BD CE DF EG
AE BF CG DH
AF BG CH
AG BH
AH

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Joined: 25 Feb 2013
Posts: 1138
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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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19 Mar 2018, 10:00
1
dave13 wrote:
Bunuel wrote:
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

The total # of games played would be equal to the # of different pairs possible from 8 teams, which is $$C^2_{8}=28$$.

P.S. Please read and follow: http://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention ot the points #3 and #8.

Bunuel you know I got confused by your shortcut solution until figured out all possible combinations in details . you know what surprises how this expression $$C^2_{8}=28$$
excludes the possibility of playing more than one game by two distinct teams, also it exludes repeated games like AB and BA....

let 8 teams be A, B, C, D, E, F, G, H

NUMBER OF GAMES PLAYES BY TWO TEAMS AS FOLLOWS:

AB BC CD DE EF
AC BD CE DF EG
AE BF CG DH
AF BG CH
AG BH
AH

Hi dave13

it is clearly mentioned in the question that each team plays against other team only Once. Hence you can safely use the formula provided by Bunuel. and if we say A plays against B then its same as saying B plays against A so order does not matter here. Hence there will be only one combination with A & B taken together and not two different combinations as stated by you AB & BA.
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Joined: 01 Mar 2019
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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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23 Mar 2019, 09:36
Since the order of the teams doesn't matter, this is a combination problem. Specifically, how many ways can 2 teams be picked from a pool of 8 (8 choose 2).

$$\frac{n!}{(n-k)!(k)!}$$

Where: n = number of items in pool; k = number of items to pick

$$\frac{8!}{(8-2)!2!} \rightarrow \frac{8!}{6!2!} \rightarrow \frac{56}{2} \rightarrow 28$$

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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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26 Mar 2019, 08:31
Experts please comment on my way of solution. I think combinatorics formulas are often restrictive and confusing. I solved this problem by the following way:

So, there are 8 teams and each team plays with each team, meaning that each team plays 7 games (except with itself, of course). So, there are 8*7= 56 games (counting as if only one team plays a game) will be played in total. If a game is played by 2 teams, so there should be 56/2=28 games as a result.

Is this a viable mehtod?
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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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26 Mar 2019, 12:11
Hi Mehemmed,

YES - your way is a valid way to approach this question. As you continue to study, you'll find that most questions in the Quant and Verbal sections can be approached in more than one way. Thus, maximizing your performance on Test Day involves more than just answering questions correctly - you have to ALSO be efficient with your approach. By extension, honing multiple skills (so that you can choose which approach is easiest on any given question) is an idea that you might want to implement in your broader study plan.

GMAT assassins aren't born, they're made,
Rich
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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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27 Mar 2019, 18:06
Yes and no. If you think because a game is played by 2 teams, thus it means dividing by 2, then no. Since 2 here really means 2!. The actual reason for dividing 56 by 2 is that when we find 8*7 = 56, each game is counted twice. For example, if a game is played by 3 teams, then it should be divided by 3!, not the number 3.
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Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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27 Mar 2019, 23:18
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

If each team played each other twice: 8(no of teams) *7(no of teams -1)
If each team played each other once: 8*7/2 = 28
OA:C
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Joined: 09 Nov 2018
Posts: 3
Re: There are 8 teams in a certain league and each team plays each of the  [#permalink]

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27 Mar 2019, 23:19
sarb wrote:
There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

A. 15
B. 16
C. 28
D. 56
E. 64

If each team played each other twice: 8(no of teams) *7(no of teams -1)
If each team played each other once: 8*7/2 = 28
OA:C
Re: There are 8 teams in a certain league and each team plays each of the   [#permalink] 27 Mar 2019, 23:19

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