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

Question

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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Qoofi · Answer

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

WillEconomistGMAT · Answer

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!

Bunuel · Answer

Similar questions to practice: how-many-diagonals-does-a-polygon-with-21-sides-have-if-one-101540.html if-10-persons-meet-at-a-reunion-and-each-person-shakes-hands-110622.html 10-business-executives-and-7-chairmen-meet-at-a-conference-126163.html how-many-different-handshakes-are-possible-if-six-girls-129992.html 15-chess-players-take-part-in-a-tournament-every-player-55939.html there-are-5-chess-amateurs-playing-in-villa-s-chess-club-127235.html if-each-participant-of-a-chess-tournament-plays-exactly-one-142222.html there-are-8-teams-in-a-certain-league-and-each-team-plays-134582.html there-are-8-teams-in-a-certain-league-and-each-team-plays-132366.html Hope it helps.

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

Answer: D

TheNightKing · Answer

9+8+7+.....+1 = (8*9)/2 = 36

MathRevolution · Answer

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

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