Question 15
The numbers $1,$ $2,$ $3,$ $4,$ $5,$ $6,$ $7,$ and $8$ are randomly written on the faces of a regular octahedron so that each face contains a different number. The probability that no two consecutive numbers, where $8$ and $1$ are considered to be consecutive, are written on faces that share an edge is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$