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

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

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New post 25 Aug 2017, 23:46
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:
https://www.khanacademy.org/math/precal ... mbinations

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

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New post 13 Oct 2017, 23:06
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





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

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New post 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 [#permalink]

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New post 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/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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Re: There are 8 teams in a certain league and each team plays [#permalink]

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New post 25 Dec 2017, 20:07
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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/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   [#permalink] 25 Dec 2017, 20:07

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