Permutations around an isosceles triangle I am trying to understand how permutations work around an isosceles triangle. I have heard and read online about such situations, though could not understand that some arrangements which appear different are treated as the same arrangement. 
Problem
A table whose table top is an isosceles triangle has vertices A,B and C with AB =  AC. Eight persons P1, P2, P3, P4, P5, P6, P7 and P8 are to be seated around this table. Only 3 persons can sit along sides AB or AC and 2 persons along side BC.
In trying to solve the above problem, I came up with 2 scenarios as shown in image below. I am not sure if the permutation on left side is same as permutation on right side.
Question
In the two permutations shown in image below, is the left permutation treated as same as the right permutation? If yes, then why are they considered the same arrangement?

 A: I think all the positions in the above diagrams are different from each other.  For example, If you take a circle with $n$ chairs, the first person can sit at any of these positions in only one way as each position is same.  Now the remaining $n-1$ persons sit at $n-1$ positions in $(n-1)!$ ways. 
Let us consider an equilateral triangle and we need to sit $9$ persons, $3$  persons per side.

In the diagram you can see that positions $1, 4, 9$ are same.  Similarly, $2, 5, 8$ are same. Also, $3, 6, 7$ are same. Therefore, considering all positions are different, total arrangements are $9!$ but 3 positions are same. So we need to divide by 3. Answer is $\dfrac{9!}{3}$ = $3\times 8!$.  
Or you can assume all are similar positions, then total arrangements are $8!$ but there are 3 different positions per side. Left, middle, right. So again answer is $3 \times 8!$
Coming to your question, though there are two equal sides, all positions are different.  For example, second person to the right of $p3$ is sitting in shorter side in one diagram, and in the other diagram, he is in the longer side. So both are different. Only in the case of garland, the above positions are equal. But when it comes to seating arrangements, these two are different. So total arrangements are $8!$
A: Both are same. As we have any person can sit on any place. 
If we don't have given conditions about how to arrange people then we don't take care of arrangements. 
