Question

Permutations!!

Answer 1

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