GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
A television advertising break is to consist of six 30-second advertis
[#permalink]
22 Jan 2021, 08:32
22 Jan 2021, 08:32
Expert Reply
2
Bookmarks
00:00
Question Stats:
68% (01:31) correct
31% (03:35) wrong based on 16 sessions
Hide Show timer Statistics
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A television advertising break is to consist of six 30-second advertis
[#permalink]
27 Jan 2021, 05:55
27 Jan 2021, 05:55
2
1
Bookmarks
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.
RELATED VIDEO
Re: A television advertising break is to consist of six 30-second advertis
[#permalink]
07 Jul 2024, 16:52
07 Jul 2024, 16:52
Hello from the GRE Prep Club BumpBot!
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
