MBA.Aspirant wrote:In how many ways can Ann, Bea, Cam, Don, Ella, and Fey be seated such that Ann and Bea cannot be seated next to each other?
A)240
B)360
C)480
D)600
E)720
Please explain in detail - Experts are welcome to reply
Good arrangements = total arrangements - bad arrangements.
Total arrangements:
Number of ways to arrange 6 elements = 6!.
Bad arrangements:
A bad arrangement seats Ann adjacent to Bea.
With AB as a single element, the number of ways to arrange the 5 elements AB, C, D, E and F = 5!.
Since AB can be reversed to BA, we multiply by 2:
2*5!.
Good arrangements = total-bad = 6! - 2*5! = 5!*(6-2) = 120*4 = 480.
The correct answer is
C.
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