Since the problem specifically stated that the people
gather around the table, therefore we assume a circular table hence a circular
formation of gathering. Since the
arrangement is important therefore we use the permutation.
nPr = n! / (n – r)!
However before we proceed with our calculation we MUST
first affix a reference point since the formation is circle. Imagine that the
reference point is the 1st point made when you draw a circle, so it
is the both the 0 degrees and the 360 degrees.
Let us say that one of the actors is the reference point.
So there are now only 8 actors which places can be interchanged. Since all
actors have to sit together, hence the arrangements are:
8P8 = 8! / (8 – 8)! = 40,320
Now since there are 13 total people, therefore the
arrangements of the other 4 people are:
4P4 = 4! / (4 – 4)! = 24
We multiply all to get the total number of arrangements:
Total arrangements = 40320 * 24 * 1 (1 is the reference point)
Total arrangements = 967,680
