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

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There are 8 teams in a certain league and each team plays [#permalink] New post 17 Jun 2012, 02:52
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2012, 02:56, edited 1 time in total.
Edited the question and added the OA.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 18 Nov 2012, 20:09
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These type of problems can be solved with a simple diagram.

1. Draw a table consisting of 8 columns and 8 rows.
2. Divide the table by a diagonal and count the number of spaces including the half spaces only on one side of the diagonal.
3. The number should be 28.


I tried uploading the diagram but unsuccessful.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 17 Jun 2012, 02:57
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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.

Answer: C.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention ot the points #3 and #8.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 16 Nov 2012, 03:19
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Sachin9 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.

Answer: C.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention ot the points #3 and #8.

I would like to learn about C^2_{8}=28. Manhattan Book doesn't discuss this approach. They have anagram approach.


Well the game is played by 2 teams. How many games are needed if there are 8 teams and each team plays each of the other teams exactly once? The number of games will be equal to the number of different pairs of 2 teams we can form out of 8 teams (one game per pair). How else?

Similar questions to practice:
how-many-diagonals-does-a-polygon-with-21-sides-have-if-one-101540.html
if-10-persons-meet-at-a-reunion-and-each-person-shakes-hands-110622.html
10-business-executives-and-7-chairmen-meet-at-a-conference-126163.html
how-many-different-handshakes-are-possible-if-six-girls-129992.html
15-chess-players-take-part-in-a-tournament-every-player-55939.html
there-are-5-chess-amateurs-playing-in-villa-s-chess-club-127235.html
if-each-participant-of-a-chess-tournament-plays-exactly-one-142222.html

Hope it helps.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 31 Jan 2013, 00:37
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it is not easy and is harder if we are on the test date.

there are 8 team
to take out 2 teams, IF ORDER MATTERS we have 8*7
but in fact order does not matter

8*7/2=28

princeton gmat book explain this point wonderfully.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 16 May 2013, 03:33
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mywaytomba wrote:
Bunuel wrote:

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


Hi Bunuel,

I have seen that you are using this formula/approach to solve most of the combination questions. Could you please explain, in general, how do you use this formula?

Thanks a lot.


Check combinatorics chapter of Math Book for theory: math-combinatorics-87345.html

Also check some questions on combinations to practice:
DS: search.php?search_id=tag&tag_id=31
PS: search.php?search_id=tag&tag_id=52

Hard questions on combinations and probability with detailed solutions: hardest-area-questions-probability-and-combinations-101361.html (there are some about permutation too)

Hope it helps.
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COLLECTION OF QUESTIONS:
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 14 Nov 2012, 05:23
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.

Answer: C.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention ot the points #3 and #8.

I would like to learn about C^2_{8}=28. Manhattan Book doesn't discuss this approach. They have anagram approach.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 15 Nov 2012, 22:27
Hi Bunnel,

I would also like to learn this approach. Can u help me?

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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 28 Dec 2012, 05:59
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


=\frac{8!}{2!6!}=4*7 = 28

Answer: C
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 16 May 2013, 00:13
Bunuel wrote:

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


Hi Bunuel,

I have seen that you are using this formula/approach to solve most of the combination questions. Could you please explain, in general, how do you use this formula?

Thanks a lot.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 17 May 2013, 20:18
pranav123 wrote:
These type of problems can be solved with a simple diagram.

1. Draw a table consisting of 8 columns and 8 rows.
2. Divide the table by a diagonal and count the number of spaces including the half spaces only on one side of the diagonal.
3. The number should be 28.


I tried uploading the diagram but unsuccessful.


That's one of those tips that can make my life easier. I'm book marking this page. Thanks.
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 26 Dec 2013, 22:04
Lets assume the question asks There are 8 teams in a certain league and each team
plays each of the other teams exactly twice. If each
game is played by 2 teams, what is the total number
of games played?

Then is 28*2 the correct approach?
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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 27 Dec 2013, 02:08
Expert's post
theGame001 wrote:
Lets assume the question asks There are 8 teams in a certain league and each team
plays each of the other teams exactly twice. If each
game is played by 2 teams, what is the total number
of games played?

Then is 28*2 the correct approach?


Yes. Check here: 15-chess-players-take-part-in-a-tournament-every-player-55939.html and here: there-are-8-teams-in-a-certain-league-and-each-team-plays-132366.html

Similar questions to practice:
how-many-diagonals-does-a-polygon-with-21-sides-have-if-one-101540.html
if-10-persons-meet-at-a-reunion-and-each-person-shakes-hands-110622.html
10-business-executives-and-7-chairmen-meet-at-a-conference-126163.html
how-many-different-handshakes-are-possible-if-six-girls-129992.html
15-chess-players-take-part-in-a-tournament-every-player-55939.html
there-are-5-chess-amateurs-playing-in-villa-s-chess-club-127235.html
if-each-participant-of-a-chess-tournament-plays-exactly-one-142222.html
there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html
there-are-8-teams-in-a-certain-league-and-each-team-plays-132366.html
in-a-kickball-competition-of-9-teams-how-many-possible-ma-161846.html

Hope it helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: There are 8 teams in a certain league and each team plays [#permalink] New post 12 Sep 2014, 05:36
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



total 8 teams & each game by 2 pair then 8C2
Re: There are 8 teams in a certain league and each team plays   [#permalink] 12 Sep 2014, 05:36
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