There are 16 teams in a tournament. If during the first round, each te

Question

There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

Bunuel · Accepted Answer

There are 16 teams in a tournament. If during the first round, each team plays every other team exactly once, how many games will be played in the first round?

A.15
B.30
C.120
D.240
E.256

Let me offer anothe solution, which might help to clear your doubt.

The total number of games played would be equal to the number of different pairs (groups of two) possible from 16 teams, which is  C^2_{16}=\frac{16!}{2!14!}=120 .

Answer: C.

chetan2u · Answer

this Q is a copy of VERITA's Q or verita's Q is a copy of this Q if the source have been mentioned correctly 
 https://gmatclub.com/forum/there-are-16-teams-in-a-soccer-league-and-each-team-plays-each-of-the-205437.html?fl=similar

Surprisingly whosoever copied has not even changed the number of teams .....

Choose two teams out of 16 - 16C2 = \frac{16!}{14!2!}= \frac{16*15}{2}= 120

FacelessMan · Answer

This is again a combinations questions since the order does not matter.

Number of ways to pick 2 teams from a total of 16 = 16C2 = 16!/14!*2! = 120. Hence C.

AbdurRakib · Answer

Really!
However

This Question appeared to me on my Kaplan Test Prep CAT

Thanks

Nathanlambson · Answer

Can someone explain to me why we divide the 16 * 15 by 2? Is it because two teams are playing?

Bunuel · Answer

Chakolate · Answer

You divide by two because if A shakes hands with B, then B is also shaking hands with A, so 16*15 counts each handshake twice.

EMPOWERgmatRichC · Answer

Hi All,

You can actually answer this question without any complex math, as long as you take the proper notes.

We're told that 16 teams each play one another once. We're asked for the total number of games played. For the sake of organization, I'm going to name the 16 teams...

ABCDE FGHIJ KLMNO P

Team A will play each of the other 15 teams = 15 games
Team B already played Team A, so Team B plays the other 14 teams = an additional 14 games
Team C already played Teams A and B, so Team C plays the other 13 teams = an additional 13 games
Etc.

Thus, the total number of games played will be... 15+14+13....+2+1+0. Using 'bunching' you end up with (15)(8) = 120 total games played.

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

singhabhijeet · Answer

If you don't know the combination formula you can still give a try. As I did with little bit logical reasoning.

Note : It's always good to use proper method / formula.

# of teams = 16. 
 
We have 5 AC.

A.15
B.30
C.120
D.240
E.256

Eliminate option A and B as the number is too low. 
Eliminate option E (16 * 16 = 256) max possible matches

Options left C & D.

If we roughly guess double entries (e.g Team1 vs Team2 = Team2 vs Team1), the number is going to be more than 16.
Hence, eliminate option D.

Ans: Option C

JeffTargetTestPrep · Answer

Since there are 16 teams and each team plays every other team once, the number of games played in the first round is 16C2 =16!/  = (16 x 15)/2! = 8 x 15 = 120 games.
 
Answer: C

Praveenksinha · Answer

The total number of games played would be equal to two selecting two teams out of 16 team

16C2=16!14!2!=16∗152=120

bumpbot · Answer

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There are 16 teams in a tournament. If during the first round, each te

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