Seven basketball teams play in a league against each other. At the end of the season, how many different arrangements

[BTGmoderatorDC]

Seven basketball teams play in a league against each other. At the end of the season, how many different arrangements are there for the top 3 teams in the rankings?

A. 6
B. 42
C. 210
D. 5,040
E. 50,450


OA C

Source: Princeton Review

[Brent@GMATPrepNow]

Seven basketball teams play in a league against each other. At the end of the season, how many different arrangements are there for the top 3 teams in the rankings?

A. 6
B. 42
C. 210
D. 5,040
E. 50,450


OA C

Source: Princeton Review

Take the task of arranging the top 3 teams and break it into stages.

Stage 1: Select the 1st place team
There are 7 teams to choose from, so we can complete stage 1 in 7 ways

Stage 2: Select the 2nd place team
Since already selected a team in stage 1, there are now 6 teams remaining to choose from.
So, we can complete stage 2 in 6 ways

Stage 3: Select the 3rd place team
There are now 5 teams remaining to choose from.
So, we can complete stage 3 in 5 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus arrange the top 3 teams) in (7)(6)(5) ways (= 210 ways)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

[swerve]

Seven basketball teams play in a league against each other. At the end of the season, how many different arrangements are there for the top 3 teams in the rankings?

A. 6
B. 42
C. 210
D. 5,040
E. 50,450


OA C

Source: Princeton Review

It's simply 7P3 = 7!/(7-3)! = 210. Selecting 3 out of 7 when the order of the selection matters.

Therefore, C