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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
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A television advertising break is to consist of six 30-second advertis
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22 Jan 2021, 08:32
22 Jan 2021, 08:32
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A television advertising break is to consist of six 30-second advertisements. If the second, fourth, and sixth of the 30-second spots are to be filled with three different advertisements for company X and the other spots are to be filled with one advertisement each for companies A, B, and C, in how many different ways can the six advertisements be ordered?
(A) 729
(B) 720
(C) 120
(D) 36
(E) 24
(A) 729
(B) 720
(C) 120
(D) 36
(E) 24
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Re: A television advertising break is to consist of six 30-second advertis
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27 Jan 2021, 05:55
27 Jan 2021, 05:55
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GeminiHeat wrote:
A television advertising break is to consist of six 30-second advertisements. If the second, fourth, and sixth of the 30-second spots are to be filled with three different advertisements for company X and the other spots are to be filled with one advertisement each for companies A, B, and C, in how many different ways can the six advertisements be ordered?
(A) 729
(B) 720
(C) 120
(D) 36
(E) 24
(A) 729
(B) 720
(C) 120
(D) 36
(E) 24
Take the task of filling the 6 advertisement spots and break it into stages.
Stage 1: Select an ad for the 1st advertisement spot
We have 3 options (ads from companies A, B or C)
So, we can complete stage 1 in 3 ways
Stage 2: Select an ad for the 2nd advertisement spot
This must be one of the 3 ads from company X
So we can complete stage 2 in 3 ways
Stage 3: Select an ad for the 3rd advertisement spot
We now have 2 options remaining, since we already selected one of the ads from companies A, B or C in stage 1.
So we can complete stage 3 in 2 ways
Stage 4: Select an ad for the 4th advertisement spot
This must be one of the 2 remaining ads from company X
So we can complete stage 4 in 2 ways
Stage 5: Select an ad for the 5th advertisement spot
We now have 1 option remaining, since we already selected two of the ads from companies A, B or C.
So we can complete stage 5 in 1 way
Stage 6: Select an ad for the 6th advertisement spot
This must be the 1 remaining ad from company X
So we can complete stage 6 in 1 way
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus fill all six advertising spots) in (3)(3)(2)(2)(1)(1) ways (= 36 ways)
Answer: D
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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Re: A television advertising break is to consist of six 30-second advertis
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07 Jul 2024, 16:52
07 Jul 2024, 16:52
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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