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30 Oct 2019, 02:47
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D
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63% (01:13) correct
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Six state governors meet at an annual convention. They line up in random order to pose for a photograph. If the governors of Alaska and Hawaii are among the six governors, how many different ways can the governors line up for the picture so that these two governors are adjacent?
A. 5
B. 10
C. 120
D. 240
E. 720
A. 5
B. 10
C. 120
D. 240
E. 720
Updated on: 17 May 2021, 08:33
Originally posted by BrentGMATPrepNow on 30 Oct 2019, 07:20.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:33, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:33, edited 1 time in total.
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Bunuel
Six state governors meet at an annual convention. They line up in random order to pose for a photograph. If the governors of Alaska and Hawaii are among the six governors, how many different ways can the governors line up for the picture so that these two governors are adjacent?
A. 5
B. 10
C. 120
D. 240
E. 720
A. 5
B. 10
C. 120
D. 240
E. 720
Let A, B, C, D, E, H represent the 6 governors (A and H stand for Alaska and Hawaii)
Now wake the task of arranging the letters and break it into stages.
Stage 1: Glue A and H together.
Note, this will ensure that A and H are adjacent.
There are 2 ways to glue A and H together: AH and HA
So we can complete stage 1 in 2 ways
IMPORTANT: We now have 5 "things" to arrange. They are: B, C, D, E and the A+H combo
Stage 3: arrange the 5 "objects" in a row
We can arrange n different objects in n! ways.
So, we can arrange the 5 objects in 5! ways (= 120 ways)
By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus arrange all 6 governors) in (2)(120) ways (= 240 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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30 Oct 2019, 08:15
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Bunuel
Six state governors meet at an annual convention. They line up in random order to pose for a photograph. If the governors of Alaska and Hawaii are among the six governors, how many different ways can the governors line up for the picture so that these two governors are adjacent?
A. 5
B. 10
C. 120
D. 240
E. 720
A. 5
B. 10
C. 120
D. 240
E. 720
\(A B C E( E F)\)
Let's consider the two people (E and F) as a single unit, we have the following arranglement \(A B C D ( E F )\) = 5!*2! => 120*2 = 240 , Answer must be (D)
