Wait, Plato, let me rephrase my question.
I have 7 doors and once I have entered one, I must exit through another. How many ways can I enter and exit through the doors?
Is my answer now correct?
I am translating these from Icelandic so sometimes I get some details wrong, unfortunately.
Don't be disheartened, Paze. Mathematics like this requires a lot of thought, as opposed to just a "plug-and-chug" approach seen in calculus courses. This sort of mathematics just requires A LOT of practice. You'll eventually get accustomed to the thought processing required by these sort of problems. Good luck with your endeavors.
Problems like this rely heavily on the "multiplication property"- if event A can happen in n ways and B can happen, independently of A, in m ways then A and B can both happen in mn ways. You can enter through any of 7 doors so "entering" can happen in 7 ways. No matter what door you entered through there are then 6 doors you can leave through. There are 7(6)=42 ways to both enter and leave through different doors.
Hello, Paze!
I have 7 doors. I enter through one, but have to exit through another.
I assume that the question is:
. . In how many ways can I pass through all the doors exactly once?
Just talk your way through it . . .
. . . . You have 7 choices of doors for entering.
Then you have 6 choices of doors for exiting.
Then you have 5 choices of doors for entering.
Then you have 4 choices of doors for exiting.
Then you have 3 choices of doors for entering.
Then you have 2 choices of doors for exiting.
Then you have 1 choice of doors for entering.
Therefore . . .
Well the question just asked for 42, e.g. how many times can I enter and exit but I expanded upon my initial view of the problem and I am now trying to confirm my suspicion.
I am wondering: How many different ways of entering and exiting can I perform? I can enter through door A and exit through door B. I can enter through door A again and exit through door C or I could have entered through door A and exited through door B and then entered through door A again and exited through door B. These would be two different scenarios. How many scenarios can I make like this? I don't even understand my own question anymore. I'm trying to set it up but I fail to see it. I understand your solutions and thank you very much. I'm just having issues wrapping my head around probability, that's all.