Problem Solving

There are 16 teams in a soccer league, and each team plays each of the others once. Given that each game is played by two teams, how many total games will be played?

A) 256
B) 230
C) 196
D) 169
E) 120

Another approach (other than 16C2) is this:

If we ask each team, "How many teams did you play?" we'll find that each team played 15 teams, which gives us a total of 240 games (since 16 x 15 = 240).

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 counts it as a game.

So, to account for the duplication, we'll divide 240 by 2 to get [spoiler]120 (E)[/spoiler]
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Here are two related questions:
https://www.beatthegmat.com/ugghhh-i-pic ... 67675.html
https://www.beatthegmat.com/number-of-ha ... 00109.html


Cheers,
Brent

Hi All,

This question can be answered in a couple of different ways. If you know the Combination Formula, then you can use that...

N!/[K!(N-K)!] where N is the total number of Teams and K is the Subgroup.

In this prompt, N = 16 and K = 2...

16!/[2!(14!)] =

(16)(15)/(2)(1) =

120 different games played

You can also use 'brute force' and a bit of logic to answer the question....

Let's call the teams...ABCDE FGHIJ KLMNO P

Team A plays each of the other 15 teams, so that's 15 games.
Team B already played Team A, so it plays 14 OTHER games.
Team C already played Teams A and B, so it plays 13 OTHER games.
Team D already played Teams A, B and C, so it plays 12 OTHER games.
Etc.

The sum of all of these games is...
15+14+13.....+3+2+1 = 120

Final Answer: E

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