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
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If the President and Vice President must sit next to each ot
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Anaira Mitch
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Let the 6 people be P, V, A, B, C and D, where P = president and V = vice-president.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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
