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Jack is making a list of his 5 favorite cities. He will choose 3 citie
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21 Oct 2021, 09:31
21 Oct 2021, 09:31
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34% (01:27) correct
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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
A. 30
B. 360
C. 1,800
D. 3,600
E. 6,720
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Re: Jack is making a list of his 5 favorite cities. He will choose 3 citie
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21 Oct 2021, 09:42
21 Oct 2021, 09:42
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Carcass 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
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
Stage 2: Select 2 European cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 2 cities from 3 cities in 3C2 ways (3 ways)
So, we can complete stage 2 in 3 ways
Stage 3: Arrange the 5 selected cities
We can arrange n unique objects in n! ways.
So, we can arrange the 5 selected cities in 5! ways (120 ways)
We can complete this stage in 120 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create our list) in (10)(3)(120) ways (= 3600 ways)
Answer: D
Re: Jack is making a list of his 5 favorite cities. He will choose 3 citie
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22 Jan 2022, 06:32
22 Jan 2022, 06:32
How is this a combination question? They have asked us to rank according to the cities right?
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
Stage 2: Select 2 European cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 2 cities from 3 cities in 3C2 ways (3 ways)
So, we can complete stage 2 in 3 ways
Stage 3: Arrange the 5 selected cities
We can arrange n unique objects in n! ways.
So, we can arrange the 5 selected cities in 5! ways (120 ways)
We can complete this stage in 120 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create our list) in (10)(3)(120) ways (= 3600 ways)
Answer: D
GreenlightTestPrep wrote:
Carcass 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
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
Stage 2: Select 2 European cities
Since the order in which we SELECT the cities does not matter, we can use combinations.
We can select 2 cities from 3 cities in 3C2 ways (3 ways)
So, we can complete stage 2 in 3 ways
Stage 3: Arrange the 5 selected cities
We can arrange n unique objects in n! ways.
So, we can arrange the 5 selected cities in 5! ways (120 ways)
We can complete this stage in 120 ways.
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create our list) in (10)(3)(120) ways (= 3600 ways)
Answer: D
