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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 [#permalink]

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20 Feb 2011, 09:13
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html
[Reveal] Spoiler: OA

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Kudos [?]: 1764 [0], given: 376

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

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20 Feb 2011, 09:17
Number of ways 2 teams can be selected out of 8 teams:

$$C^8_2=\frac{8*7}{2}=28$$

Ans:"C"
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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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20 Feb 2011, 20:20
GMATD11 wrote:
sol

8th team will play 7 games with 7 teams, so total number of games played by 8th team is 7
similarly 7----------------6------------6------------------------------------------ 7----------- 6
--------6----------------5------------5------------------------------------------ 8----------- 5
nd so on

total games played= 7+6+5+4+3+2+1=28

any other optimal sol.

Your reasoning is perfect.... Just that to perform 7+6+5+4+3+2+1, use the formula n(n+1)/2 where n = 7.
7*8/2 = 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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21 Feb 2011, 11:41
in what cases u will use the formula n(n+1)/2?
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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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21 Feb 2011, 11:48
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KUDOS
144144 wrote:
in what cases u will use the formula n(n+1)/2?

Just to add first n natural numbers; that's all

1+2+3+4+5
Here n=5; Sum = n(n+1)/2 = 5*6/2=15

1+2+3+4+5+6+7+8+9
Here n=5; Sum = n(n+1)/2 = 9*10/2=45

In the above example;
7+6+5+4+3+2+1
Sum of natural numbers from 1 to 7 = 7*8/2 = 56/2 = 28.

It easy this way rather than adding every number.
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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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17 Aug 2015, 10:28
GMATD11 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 $$C^2_{8}=28$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html
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Re: There are 8 teams in a certain league and each team plays each of the   [#permalink] 17 Aug 2015, 10:28
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# There are 8 teams in a certain league and each team plays each of the

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