Bunuel wrote:

In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

A. 24

B. 48

C. 56

D. 72

E. 96

We can use the following formula:

Total number of ways to arrange the 5 people = (number of arrangements when Bob sits next to Ann) + (number of arrangements when Bob does not sit next to Ann)

Let’s determine the number of arrangements when Bob sits next to Ann.

We can denote Ann, Bob, Chuck, Don, and Ed as A, B, C, D, and E, respectively.

If Ann and Bob must sit together, we can consider them as one person [AB]. For example, one seating arrangement could be [AB][C][D][E]. Thus, the number of ways to arrange four people in a row is 4! = 24.

However, we must also account for the ways we can arrange Ann and Bob, that is, either [AB] or [BA]. Thus, there are 2! = 2 ways to arrange Ann and Bob.

Therefore, the total number of seating arrangements is 24 x 2 = 48 if Ann and Bob DO sit next to each other.

Since there are 5 people being arranged, the total number of possible arrangements is 5! = 120.

Thus, the number of arrangements when Bob does NOT sit next to Ann is 120 - 48 = 72.

Answer: D

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Jeffery Miller

Head of GRE Instruction

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