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Jack is making a list of his 5 favorite cities. He will choose 3 citie [#permalink]

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09 May 2017, 12:48

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Question Stats:

46% (01:19) correct 54% (00:56) wrong based on 52 sessions

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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?

Re: Jack is making a list of his 5 favorite cities. He will choose 3 citie [#permalink]

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09 May 2017, 13:12

Ways of choosing his top 3 american cities from a list of 5: 5c3 Ways of choosing his top 2 american cities from a list of 3: 3c2 Ways of arranging them in order from 1 to 5: 5!

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

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

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Re: Jack is making a list of his 5 favorite cities. He will choose 3 citie
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03 Nov 2017, 08:48