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amgelcer
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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amgelcer
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 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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Total teams: n

Number of matches: \(\frac{n(n-1) }{ 2}\)

=> n = 9. Hence, number of matches: \(\frac{9 * 8 }{ 2}\) = 36

Answer D
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