Problem Solving

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?

A) 120
B) 240
C) 300
D) 360
E) 720

If the President (P) and Vice President (v) must sit next to each other, let's physically "glue" them together to form a single entity: Pv

So, we must arrange Pv and 4 other members of the Board.
In other words, we must arrange a total of 5 entities in a row.
We can do so in 5! ways (120 ways)

HOWEVER, the correct answer is not A, because we've only considered one way to "glue" the President (P) and Vice President (v) together.
In the first configuration, Pv, the President is to the LEFT of the Vice President.

Notice that we can also glue them the other way (vP), where the President is to the RIGHT of the Vice President.
Now we must arrange vP and 4 other members of the Board.
We can do so in 5! ways (120 ways)

So, the TOTAL number of arrangements = 120 + 120 = 240

Answer: B

Cheers,
Brent

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

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

We need to determine how many ways the President and Vice President can sit next to each other in a row with 4 other members of the board. Since order matters, we have a permutation problem.

We can denote the President as P, the Vice President as V, and the four other members as A, B, C, and D. Thus, we are arranging the members as the following:

[V-P] - [A] - - [C] - [D]

(Note:since the President and Vice President must sit together, we have included them in one bracket.)

Since we have 5 brackets, we can arrange those 5 brackets in 5! or 120 ways. However, we must account for the individual arrangement of the President and Vice President, and they can be arranged in 2! or 2 ways, i.e., [V-P] or [P-V].

Thus, when the President and Vice President are sitting together, the group can be arranged in 2 x 120 = 240 ways.

Answer: B