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In a kickball competition of 9 teams, how many possible ma

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In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 19 Oct 2013, 06:46
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In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

------------
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Re: In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 19 Oct 2013, 07:00
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

------------
Did you try this? How about +KUDOS for me?


Hi amgelcer.

Each team can play with each other in 9C2 ways

9C2 = 9*8 / 1*2 = 36

Option D

Hope it helped

Cheers
Qoofi
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Re: In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 19 Oct 2013, 08:58
Qoofi wrote:
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

------------
Did you try this? How about +KUDOS for me?


Hi amgelcer.

Each team can play with each other in 9C2 ways

9C2 = 9*8 / 1*2 = 36

Option D

Hope it helped

Cheers
Qoofi


Qoofi is correct. In case you need a general reminder of the combination formula as well, here it is:

nCr, read "n choose r" is n!/r!(n-r)!

Here, then we have 9 teams chosen 2 at a time. So 9C2 is 9!/2!(9-2)! --> 9!/2!7! --> 9*8/2.

That may help on future combination problems. Cheers!
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Re: In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 20 Oct 2013, 13:25
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

------------
Did you try this? How about +KUDOS for me?


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Re: In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 08 Sep 2019, 09:06
Top Contributor
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54



A DIFFERENT approach

If each of the 9 teams plays every team, then each team plays 8 games (since a team can't play itself)
So, the total number of games = (9)(8) = 72

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 72 by 2 to get 36

Answer: D

Cheers,
Brent
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Re: In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 12 Sep 2019, 11:27
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

------------
Did you try this? How about +KUDOS for me?


The total possible number of matches is 9C2 = 9! / (2! x 7!) = (9 x 8) / 2 = 36.

Answer: D
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In a kickball competition of 9 teams, how many possible ma  [#permalink]

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New post 07 Oct 2019, 20:44
amgelcer wrote:
In a kickball competition of 9 teams, how many possible matches can each team play with each other?

(A) 9
(B) 16
(C) 24
(D) 36
(E) 54

9+8+7+.....+1 = (8*9)/2 = 36
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In a kickball competition of 9 teams, how many possible ma   [#permalink] 07 Oct 2019, 20:44
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