Question 10
We arrange the following seven $4$-digit numbers: $2021$, $2022$, $2023$, $2024$, $2025$, $2026$ and $2027$ in a row, in such a way that any two adjacent numbers are relatively prime. For example: $2027,2022,2023,2024,2025,2026,2021$ is one such arrangement.
How many different such arrangements are there?
How many different such arrangements are there?