To count CIRCULAR arrangements:
1. Place one element in the circle.
2. Count the number of ways to arrangement the REMAINING elements RELATIVE to the first element.
Uva@90 wrote:A,B,C,D,E go to a restaurant. there are five chairs in a Circular arrangement. in how many ways they can sit in the circular arrangement such that A and B don't want to sit together ?
A) 10
B) 12
C) 16
D) 20
E) 24
Once A has been placed at the table, we get:
Number of options for the seat to the left of A = 3. (Of the 4 remaining people, anyone but B.)
Number of options for the seat to the right of A = 2. (Of the 3 remaining people, anyone but B.)
Number of ways to arrange the 2 remaining people = 2! = 2.
To combine these options, we multiply:
3*2*2 = 12.
The correct answer is
B.
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