For circular arrangements:
1. Place someone at the table.
2. Count the number of ways to arrange the REMAINING people.
ardz24 wrote:Seven family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
A. 120
B. 240
C. 360
D. 480
E. 720
Once Michael has been placed at the table:
Number of options for Bobby = 2. (To the left or right of Michael.)
Number of ways to arrange the remaining 5 people = 5!.
To combine these options, we multiply:
2 * 5! = 2 * 120 = 240.
The correct answer is
B.
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