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A television advertising break is to consist of six 30-second advertis
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03 Feb 2017, 03:24
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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?
Re: A television advertising break is to consist of six 30-second advertis
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03 Feb 2017, 10:27
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SajjadAhmad 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
_I_ | _II_ | _III_ | _IV_ | _V_ | _VI_
The even places can be filled in 3! ways = 6 ways ( 3 Different adds of Company X ) The remaining places can be filled in 3! ways = 6 ways ( 3 Different adds of companies A, B, and C )
Thus, Total No of ways will be 6*6 = 36 ways...
Hence, Correct answer must be (D) 36.. _________________
Thanks and Regards
Abhishek....
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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
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Sajjad1994 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
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 GMAT. So, be sure to learn it.
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