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

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Intern
Joined: 09 Apr 2017
Posts: 12
Re: There are 8 teams in a certain league and each team plays [#permalink]

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26 Aug 2017, 00:46
Try this watch this, similar examples-

Try pick up from Khan academy to built the foundation for permutations and combinations.

The questions are very interesting too.

Similar questions found in:

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Intern
Joined: 13 Oct 2017
Posts: 3
Re: There are 8 teams in a certain league and each team plays [#permalink]

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14 Oct 2017, 00:06
Let me sort this in a non conventional way. Since there are 8 teams let us consider them as A,B,C,D,E,F,G,H

Now A can play with B,C,D,E,F,G,H so total 7 matches
Now B can play with all others other than itself and A since it already played with A in previous step
So total 6 matches- C,D,E,F,G,H total 6 matches
Now C can play with D,E,F,G,H. Total 5 matches
Now D can play with E,F,G,H total 4 matches
Now E can play with F,G,H total 3 matches
Now F can play with G,H total 2 matches
Now G can play with H total 1 match
So now if we add all of these
7+6+5+4+3+2+1 = 28 is our answer.

Hope this helps

Sent from my iPhone using GMAT Club Forum mobile app
Director
Joined: 17 Dec 2012
Posts: 635
Location: India
There are 8 teams in a certain league and each team plays [#permalink]

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14 Oct 2017, 02:54
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

One needs to always find n and r in permutation and combination problems. n is the total number from which you choose and r is how many you choose at a time which makes it one possibility. If the order of the entities chosen at a time, does not matter as in this case, it is nCr , otherwise it is nPr.

n and r in this problem are 8 and 2 respectively and the total number of games played is 8C2=28. Hence C.
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Senior Manager
Joined: 09 Mar 2016
Posts: 448
Re: There are 8 teams in a certain league and each team plays [#permalink]

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25 Dec 2017, 14:22
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!
Math Expert
Joined: 02 Sep 2009
Posts: 44650
Re: There are 8 teams in a certain league and each team plays [#permalink]

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25 Dec 2017, 21:07
Expert's post
1
This post was
BOOKMARKED
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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Senior Manager
Joined: 09 Mar 2016
Posts: 448
There are 8 teams in a certain league and each team plays [#permalink]

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18 Mar 2018, 08:12
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: 1060
Location: India
GPA: 3.82
Re: There are 8 teams in a certain league and each team plays [#permalink]

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19 Mar 2018, 11:00
1
KUDOS
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.
Re: There are 8 teams in a certain league and each team plays   [#permalink] 19 Mar 2018, 11:00

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