Linear Symmetry Permutations refer to Arrangements of a Given Number of Objects/Items in a Line.
In this, Every Arrangement (Permutation) and it's Corresponding Reverse Arrangement (Permutation) is considered to be a Single Arrangement (Permutation) (as they represent the Same Line).
Therefore Total Count of Linear Symmetry Permutations Without Repeatition of \(N\) Objects/Items Taking \(R\) Objects/Items at a time (where \(R\leq N\))
is Half the Count of Symmetry Independent Permutations Without Repeatition \(={\Large\frac{P(N,R)}{2}}={\Large\frac{N!}{2(N-R)!}}\) (when \(R\leq N\))
OR \(={\Large\frac{N!}{2}}\) (when \(R=N\))