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An auditor wants to conduct audits in 4 schools, of 5 different cities

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An auditor wants to conduct audits in 4 schools, of 5 different cities [#permalink] New post   Updated on: 30 Mar 2021, 11:29
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An auditor wants to conduct audits in 4 schools, of 5 different cities, in such a way that no two schools belong to same city. If in each city, there are 2 schools then in how many ways can the auditor select the schools for audit?

(A) 5
(B) 20
(C) 40
(D) 80
(E) 160
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D

Originally posted by FitnessforFriends on 30 Mar 2021, 11:21.
Last edited by Bunuel on 30 Mar 2021, 11:29, edited 1 time in total.
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Re: An auditor wants to conduct audits in 4 schools, of 5 different cities [#permalink] New post   30 Mar 2021, 22:43
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Select 4 cities out of 5 and select 1 school in each of the 4 cities

5C4*(2C1)^4=5*16=80

Option D
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Re: An auditor wants to conduct audits in 4 schools, of 5 different cities [#permalink] New post   15 Apr 2021, 11:27
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FitnessforFriends wrote:
An auditor wants to conduct audits in 4 schools, of 5 different cities, in such a way that no two schools belong to same city. If in each city, there are 2 schools then in how many ways can the auditor select the schools for audit?

(A) 5
(B) 20
(C) 40
(D) 80
(E) 160

Solution:

There are 2C1 = 2 choices of schools for each of the 4 cities he will visit and there are 5C4 = 5 ways to choose the 4 cities. Therefore, there are a total of 2 x 2 x 2 x 2 x 5 = 80 ways to visit the schools.

Answer: D
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gmatclubot
Re: An auditor wants to conduct audits in 4 schools, of 5 different cities [#permalink]
15 Apr 2021, 11:27
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