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During a season in a certain baseball league every team play

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During a season in a certain baseball league every team play  [#permalink]

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New post 13 Sep 2013, 02:19
2
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:18) correct 35% (01:14) wrong based on 241 sessions

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During a season in a certain baseball league every team plays every other team in the league 10 times. If there are ten teams in the league, how many games are played in the league in one season?

(A) 45
(B) 90
(C) 450
(D) 900
(E) 1000
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Re: During a season in a certain baseball league every team play  [#permalink]

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New post 13 Sep 2013, 02:25
siddharthkanjilal wrote:
During a season in a certain baseball league every team plays every other team in the league 10 times. If there are ten teams in the league, how many games are played in the league in one season?

(A) 45
(B) 90
(C) 450
(D) 900
(E) 1000


The total # of games played would be equal to the # of different pairs possible from 10 teams, multiplied by the # of plays which is \(C^2_{10}*10=450\).

Answer: C.
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Re: During a season in a certain baseball league every team play  [#permalink]

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New post 13 Sep 2013, 02:26
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Bunuel wrote:
siddharthkanjilal wrote:
During a season in a certain baseball league every team plays every other team in the league 10 times. If there are ten teams in the league, how many games are played in the league in one season?

(A) 45
(B) 90
(C) 450
(D) 900
(E) 1000


The total # of games played would be equal to the # of different pairs possible from 10 teams, multiplied by the # of plays which is \(C^2_{10}*10=450\).

Answer: C.


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Re: During a season in a certain baseball league every team play  [#permalink]

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New post 13 Sep 2013, 05:02
Another approach without combinations:
1) if it was one round of playing with each team, then total number is 10 (teams) * 9 (games) / 2 (get rid of pairs) = 45.
2) ten rounds = 45*10 = 450, i.e. answer C.

But I've selected 45, to be honest. Just forgot about step 2 =)
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Re: During a season in a certain baseball league every team play  [#permalink]

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New post 26 Jul 2017, 16:45
siddharthkanjilal wrote:
During a season in a certain baseball league every team plays every other team in the league 10 times. If there are ten teams in the league, how many games are played in the league in one season?

(A) 45
(B) 90
(C) 450
(D) 900
(E) 1000


If each team plays every other team exactly once, then there are 10C2 = (10 x 9)/2! = 45 games played. However, since each team plays every other team 10 times, a total of 10 x 45 = 450 games are played.

Answer: C
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Re: During a season in a certain baseball league every team play  [#permalink]

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New post 27 Jul 2018, 11:12
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Re: During a season in a certain baseball league every team play   [#permalink] 27 Jul 2018, 11:12
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