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Six state governors meet at an annual convention. They line

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Six state governors meet at an annual convention. They line [#permalink] New post 30 Dec 2017, 13:50
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Question Stats:

66% (00:40) correct 33% (01:31) wrong based on 6 sessions
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

Drill 2
Question: 1
Page: 563
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
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Joined: 07 Jun 2014
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WE: Business Development (Energy and Utilities)
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Kudos [?]: 1664 [1] , given: 396

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Re: Six state governors meet at an annual convention. They line [#permalink] New post 08 Jan 2018, 16:22
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Explanation

This is a permutation because order matters.

First, think about the positions for the 2 governors from Alaska and Hawaii. There are 5 pairs of spots they can occupy: first and second, second and third, third and fourth, fourth and fifth, or fifth and sixth.

That gives you 5 possibilities; since either governor could come first, you have a total of 5 × 2 = 10 possible ways to arrange those 2 governors. Meanwhile, for each of those options, the other governors can assume any of the remaining spots, which equals 4 × 3 × 2 × 1, or 24 possibilities.

The answer is thus 10 × 24 = 240, choice (D).
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Re: Six state governors meet at an annual convention. They line [#permalink] New post 10 Jan 2018, 01:33
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So lets use # arrangements - Restriction (that is Alaska/Hawai together) = total arrangements
For total arrangements = 6! Or 720
For Alaska Hawai to be together we can list out : 10 ways
Which leaves 4 places for all the remaining governors: 4!
10 * 4! = 240
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Re: Six state governors meet at an annual convention. They line [#permalink] New post 11 Jan 2018, 08:32
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5! * 2!
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Re: Six state governors meet at an annual convention. They line [#permalink] New post 03 Feb 2018, 04:03
Thank you.
Re: Six state governors meet at an annual convention. They line   [#permalink] 03 Feb 2018, 04:03
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Six state governors meet at an annual convention. They line

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