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Jack is making a list of his 5 favorite cities

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by BTGmoderatorDC » Fri Nov 03, 2017 6:24 am
Jack is making a list of his 5 favorite cities. He will choose 3 cities in the United States from a list of 5 candidates. He will choose 2 cities in Europe from a list of 3 candidates. How many different lists of cities, ranked from first to fifth, can Jack make?

A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720

How will i solve this kind of problem? Can some experts help me please?

OA D
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by Brent@GMATPrepNow » Fri Nov 03, 2017 7:47 am
lheiannie07 wrote:Jack is making a list of his 5 favorite cities. He will choose 3 cities in the United States from a list of 5 candidates. He will choose 2 cities in Europe from a list of 3 candidates. How many different lists of cities, ranked from first to fifth, can Jack make?

A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720
Take the task of creating a list and break it into stages.

Stage 1: Select 3 US cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 3 cities from 5 cities in 5C3 ways (10 ways)
So, we can complete stage 1 in 10 ways

If anyone is interested, we have a free video on calculating combinations (like 5C3) in your head: 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
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Mon Nov 11, 2019 1:22 pm
BTGmoderatorDC wrote:Jack is making a list of his 5 favorite cities. He will choose 3 cities in the United States from a list of 5 candidates. He will choose 2 cities in Europe from a list of 3 candidates. How many different lists of cities, ranked from first to fifth, can Jack make?

A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720

How will i solve this kind of problem? Can some experts help me please?

OA D
If the ranking doesn't matter, there are 5C3 x 3C2 lists of 5 cities. However, since, for each list of the 5 cities, there are 5! ways to rank them from first to fifth, the total number of ranked lists is:

5C3 x 3C2 x 5!

(5 x 4 x 3)/(3 x 2) x 3 x 120

10 x 3 x 120 = 3,600

Answer: D

Scott Woodbury-Stewart
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by Scott@TargetTestPrep » Mon Nov 11, 2019 1:22 pm
BTGmoderatorDC wrote:Jack is making a list of his 5 favorite cities. He will choose 3 cities in the United States from a list of 5 candidates. He will choose 2 cities in Europe from a list of 3 candidates. How many different lists of cities, ranked from first to fifth, can Jack make?

A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720

How will i solve this kind of problem? Can some experts help me please?

OA D
If the ranking doesn't matter, there are 5C3 x 3C2 lists of 5 cities. However, since, for each list of the 5 cities, there are 5! ways to rank them from first to fifth, the total number of ranked lists is:

5C3 x 3C2 x 5!

(5 x 4 x 3)/(3 x 2) x 3 x 120

10 x 3 x 120 = 3,600

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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