In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?
a) 720
b) 120
c) 108
d) 84
e) 48
a) 720
b) 120
c) 108
d) 84
e) 48
To count circular arrangements:In how many ways can 6 people A, B, C, D, E and F be seated at a round table if A cannot sit next to B or C?
a) 720
b) 120
c) 108
d) 84
e) 48
1. Place someone in the circle.
2. Count the number of ways to arrange the REMAINING people.
After A is placed in the circle:
Number of options for the seat to the left of A = 3. (Of the 5 remaining people, anyone but B or C.)
Number of options for the seat to the right of A = 2. (Of the 4 remaining people, anyone but B or C.)
Number of ways to arrange the remaining 3 people = 3! = 6.
To combine these options, we multiply:
3*2*6 = 36.
The correct number of arrangements is not among the answer choices.
What is the source of this problem?
