Hello Everyone!

Lets say we have 6 places: $\displaystyle A_1, A_2, B_1, B_2, C_1, C_2$ and we want to pass by these places in a way that we always start by $\displaystyle A_1$ and end by $\displaystyle A_2$ and that $\displaystyle X_1$ always comes after $\displaystyle X_2$. I'm thinking of $\displaystyle 4! / 4 = 6$, I know it's 6, why I used this formula is because it works for 4 places: $\displaystyle A_1, B_1, A_2, B_2$...

(1) What if each time, our trip starts by $\displaystyle B$ or $\displaystyle C$, we get a total of $\displaystyle 3*6=18$?

(2) What about when there are 8 places, is it $\displaystyle 6!/6 = 120$?

Thanks for the help!