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There are 8 teams in a certain league and each team plays each of the
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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
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Originally posted by sarb on 17 Jun 2012, 02:52.
Last edited by Bunuel on 26 Feb 2019, 03:29, edited 2 times in total.
Renamed the topic.




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Re: There are 8 teams in a certain league and each team plays each of the
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16 Nov 2012, 03:19
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: http://gmatclub.com/forum/rulesforpos ... 33935.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: http://gmatclub.com/forum/howmanydiag ... 01540.htmlhttp://gmatclub.com/forum/if10persons ... 10622.htmlhttp://gmatclub.com/forum/10businesse ... 26163.htmlhttp://gmatclub.com/forum/howmanydiff ... 29992.htmlhttp://gmatclub.com/forum/15chessplay ... 55939.htmlhttp://gmatclub.com/forum/thereare5c ... 27235.htmlhttp://gmatclub.com/forum/ifeachparti ... 42222.htmlHope it helps.
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Re: There are 8 teams in a certain league and each team plays each of the
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31 Jan 2013, 00:37
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 each of the
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17 Jun 2012, 02:57
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: rulesforpostingpleasereadthisbeforeposting133935.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 each of the
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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: rulesforpostingpleasereadthisbeforeposting133935.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 each of the
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18 Nov 2012, 20:09
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 each of the
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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 each of the
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16 May 2013, 03:33
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: mathcombinatorics87345.html Also check some questions on combinations to practice: DS: search.php?search_id=tag&tag_id=31PS: search.php?search_id=tag&tag_id=52Hard questions on combinations and probability with detailed solutions: hardestareaquestionsprobabilityandcombinations101361.html (there are some about permutation too) Hope it helps.
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Re: There are 8 teams in a certain league and each team plays each of the
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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 each of the
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27 Dec 2013, 02:08



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Re: There are 8 teams in a certain league and each team plays each of the
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SreeViji wrote: Hi Bunnel,
I would also like to learn this approach. Can u help me?
Sree Hey SreeViji, I think i have something to help you. The answer here is the combination 8C2 ( 8 teams Choose 2) which mean \frac{8!}{6!x2!} > \frac{8x7}{2} To understand that we just have to think that each of the 8 team plays against 7 other (8x7) but they play each team exactly once so we divide the total by 2. We divide by 2 because "TEAM A VS TEAM B" is the same as "TEAM B VS TEAM A" So we end up with \frac{8x7}{2}= 28 If you still have trouble with combination and permutation check out this website it's well done, http://www.mathsisfun.com/combinatorics ... tions.htmlhope it helps.



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Re: There are 8 teams in a certain league and each team plays each of the
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12 Jan 2015, 13:46
Hi All, Using the Combination Formula IS one way to approach these types of questions, but it's not the only way. Sometimes the easiest way to get to a solution on Test Day is to just draw a little picture and keep track of the possibilities.... Let's call the 8 teams: ABCD EFGH We're told that each team plays each other team JUST ONCE. Start with team A.... A plays BCD EFGH = 7 games total Team B has ALREADY played team A, so those teams CANNOT play again... B plays CD EFGH = 6 more games Team C has ALREADY played teams A and B, so the following games are left... C plays D EFGH = 5 more games At this point, you should notice a pattern: the additional number of games played is reduced by 1 each time. So what we really have is: 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 = 28 games played Final Answer: 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
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19 May 2015, 06:31
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. Hi, I don;t think we need to count the half spaces. with half space count is 36. without half space  count: 28.
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Re: There are 8 teams in a certain league and each team plays each of the
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20 May 2015, 02:10
onedayill wrote: 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. Hi, I don;t think we need to count the half spaces. with half space count is 36. without half space  count: 28. Dear onedayillYou're right! The boxes along the diagonal (these are the boxes that contribute to half spaces) represent a team playing with itself. Since that is not possible, these boxes should not be included in the counting. I noticed in the thread above that a few students had doubts about the expression 8C2. If any of the current students too have such a doubt, here's how this question could be solved visually: There are 7 ways in which Team 1 can play with another team. Similarly, there are 7 ways for each of the 8 teams to choose its playing opponent. But it's easy to see that the red zone is essentially a duplication of the blue zone. For example, (Team 1 playing with Team 2) is the same case as (Team 2 playing with Team 1) So, the correct answer will be: 8(that is, the number of teams)*7(that is, the number of ways in which each team can choose its playing opponent)/2 = 28 Hope this was useful! Best Regards Japinder
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Re: There are 8 teams in a certain league and each team plays each of the
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25 May 2016, 21:25
Attached is a visual that should help.
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Screen Shot 20160525 at 9.41.57 PM.png [ 75.15 KiB  Viewed 126164 times ]



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Re: There are 8 teams in a certain league and each team plays each of the
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16 Jun 2016, 05:00
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 We are given that there are 8 teams in a league and that each game is played by 2 teams. Note that each team does not play itself, and the order of pairing each team with its opponent doesn't matter. [For example, the pairing of (Team A vs. Team B) is identical to the pairing of (Team B vs. Team A).] The situation can therefore be solved by finding the number of combinations of 8 items taken 2 at a time, or 8C2, as follows: 8C2 = 8! / [2! x (82)!] (8 x 7 x 6!) / (2! x 6!) (8 x 7)/2! (8 x 7)/ 2 4 x 7 = 28 Answer C
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Re: There are 8 teams in a certain league and each team plays each of the
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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 There are 8 teams. If we ask each team, "How many teams did you play?" we'll find that each team played 7 teams, which gives us a total of 56 games (since 8 x 7 = 56). From here we need to recognize that each game has been COUNTED TWICE. For example, if Team A and Team B play a game, then Team A counts it as a game, and Team B ALSO counts it as a game. So, to account for the DUPLICATION, we'll divide 56 by 2 to get 28 Answer: C Cheers, Brent
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Re: There are 8 teams in a certain league and each team plays each of the
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14 Oct 2017, 01:54
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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Re: There are 8 teams in a certain league and each team plays each of the
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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 \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: http://gmatclub.com/forum/rulesforpos ... 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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Re: There are 8 teams in a certain league and each team plays each of the
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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 \(C^2_{8}=28\). Answer: C. P.S. Please read and follow: http://gmatclub.com/forum/rulesforpos ... 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) Similar questions to practice: http://gmatclub.com/forum/howmanydiag ... 01540.htmlhttp://gmatclub.com/forum/if10persons ... 10622.htmlhttp://gmatclub.com/forum/10businesse ... 26163.htmlhttp://gmatclub.com/forum/howmanydiff ... 29992.htmlhttp://gmatclub.com/forum/15chessplay ... 55939.htmlhttp://gmatclub.com/forum/thereare5c ... 27235.htmlhttp://gmatclub.com/forum/ifeachparti ... 42222.htmlhttp://gmatclub.com/forum/thereare8t ... 34582.htmlhttp://gmatclub.com/forum/thereare8t ... 32366.htmlhttp://gmatclub.com/forum/inakickball ... 61846.html http://gmatclub.com/forum/thereare8t ... 34582.html
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