Bunuel wrote:
In how many ways can Ann, Bea, Cam, Don, Ella and Fey be seated if Ann and Bea cannot be seated next to each other?
(A) 240
(B) 360
(C) 480
(D) 600
(E) 720
We can use the following formula:
Total number of ways to arrange the 6 people = (number of arrangements in which Bea sits next to Ann) + (number of arrangements in which Bea does not sit next to Ann)
Let’s determine the number of arrangements in which Bea sits next to Ann.
We can denote Ann, Bea, Cam, Don, Ella, and Fey as A, B, C, D, E, and F respectively.
If Ann and Bea must sit together, we can consider them as one person [AB]. For example, one seating arrangement could be [AB][C][D][E][F]. Thus, the number of ways to arrange five people in a row is 5! = 120.
However, we must also account for the ways we can arrange Ann and Bea, that is, either [AB] or [BA]. Thus, there are 2! = 2 ways to arrange Ann and Bea.
Therefore, the total number of seating arrangements is 120 x 2 = 240 if Ann and Bea DO sit next to each other.
Since there are 6 people being arranged, the total number of possible arrangements is 6! = 720.
Thus, the number of arrangements in which Bea does NOT sit next to Ann is 720 - 240 = 480.
Answer: C
_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club.
Read Our Reviews