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If the President and Vice President must sit next to each ot

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by GMATGuruNY » Mon Jan 02, 2017 11:08 pm
Anaira Mitch wrote:If the President and Vice President must sit next to each other in a row with 4 other members of the Board, how many different seating arrangements are possible?

120

240

300

360

720
Let the 6 people be P, V, A, B, C and D, where P = president and V = vice-president.
Since P and V must be in adjacent seats, consider [PV] a single element in the arrangement.
The number of ways to arrange the 5 elements [PV], A, B, C and D = 5! = 120.
Since P and V can swap positions -- doubling the number of possible arrangements -- we multiply by 2:
120 * 2 = 240.

The correct answer is B.
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by [email protected] » Tue Jan 03, 2017 10:52 am
Hi Anaira Mitch,

There are a couple of different ways to approach this question, depending on how you "see" the math involved. Here's a visual way to quickly get to the correct answer...

Since the President and Vice-President MUST sit next to one another in a row of 6 people, we could have the following arrangement:

P V _ _ _ _

Those remaining 4 spots are essentially a factorial...

P V 4 3 2 1

So there are 24 possible arrangements that begin with "P V." Similarly, if we reversed the position of the President and Vice-President, we'd have another 24 arrangements...

V P 4 3 2 1

That brings the total to 48 arrangements if the P and the V are in the first two spots. This pattern continues all the way down the line, as long as the P and the V are in two consecutive spots...

P V _ _ _ _
_ P V _ _ _
_ _ P V _ _
_ _ _ P V _
_ _ _ _ P V

Each option gives us 48 arrangements; since there are 5 options, there are (5)(48) = 240 possible arrangments.

Final Answer: B

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