I understand that I can find resources for combination and permutations online, but as it stands I cannot fit what I learnt online with my situation. My situation may not be unique but to me as of now it is very difficult to understand which type of permutation or combination to use, so I thought to ask here. Not asking for someone to help calculation a simple permutation (or combination), but explain how to go from my problem to deciding which one to use and then using it to find the answer.
As the topic states, my problem is that I need to find out of a possible 119 train station stops, how many different ways I can go from $3$ specific stops to all other stops.
How do I go from knowing this above to deciding to use combination or permutations, and then which type of combination or permutation thereafter. It's easier when using lottery, picking colored balls etc, but when put into a real scenario like this one its hard for me to tell if this is ordered, unordered, etc.
In any case I hope someone can shed some light to this problem. Thank you.
Let us look at the situation with $10$ stations in each line. Say you have line $1,2$ and $3$ and let us call the stations $A_1,B_1,C_1,D_1,E_1,F_1,G_1,H_1,J_1,K_1$, $A_2,B_2,C_2,D_2,E_2,F_2,G_2,H_2,J_2,K_2$ and $A_3,B_3,C_3,D_3,E_3,F_3,G_3,H_3,J_3,K_3$ respectively. Let us also assume that the station where you can change is $E_1,E_2$ and $E_3$, since this is a station that is shared by all lines it is not smart to give it three names let us call it $O$ instead (in the comments I considered them different that is how I got the number $29$).
So, say you would like to travel from $B_1$. You have $9$ different routes to reach all stations in line $1$ ($10$ if you consider "staying at $B_1$" as an "empty" route, in the comments I didnt count with this). Also we do not allow traveling back and forth like $B_1\to C_1\to D_1\to C_1\to D_1\to O$ since this makes that the problem has infinite solutions.
Let us say that we dont consider empty routes so we can reach all stations in line $1$ in $9$ ways.
Taking into account line number $2$ from $B_1$ you have to travel to $O$ and from here you have $9$ different routes, one to each of $A_2, B_2,\ldots J_2,K_2$ this is $9$ different routes.
Same goes if you would like to change to line $3$.
This means that from $B_1$ there are $9+9+9=27$ different routes you could take.
Observe that the same is true if you start from $O$, the transit station.
So if you pick $3$ starting stations you would have $27$ possible routes from each of them.
Why I was puzzled as you can see in the comments is because there is not much combinatorics included in the solution so I thought I am misunderstanding the question.
Hope I understood the question correctly.