Six 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?
Select
A) 48
B) 56
C) 64
D) 72
E) 80
Let's consider Michael and Bobby as one unit.   There are 5! possible arrangements of 5 units.   Around a table, there would be repetitions of each arrangement, so we divide by 5.   Then there are 4! arrangements around a circular table.   For each arrangement, Michael and Bobby can switch places, so we multiply by 2.   The number of arrangements is 4!*2 = 48.   The answer is 48.
<result>A</result>
Six 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?