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.
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 . . .
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.