I have 7 doors. I enter through one but have to exit through another.

The solution I've come up with is 6!*7!. Would this be the correct solution? :/

Thanks!

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- Mar 14th 2013, 07:39 AMPaze7 doors
I have 7 doors. I enter through one but have to exit through another.

The solution I've come up with is 6!*7!. Would this be the correct solution? :/

Thanks! - Mar 14th 2013, 07:46 AMPlatoRe: 7 doors
- Mar 14th 2013, 07:49 AMPazeRe: 7 doors
- Mar 14th 2013, 07:52 AMPazeRe: 7 doors
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. - Mar 14th 2013, 07:56 AMBashyboyRe: 7 doors
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.

- Mar 14th 2013, 08:30 AMHallsofIvyRe: 7 doors
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.

- Mar 19th 2013, 05:58 PMPazeRe: 7 doors
Thanks guys but what I mean is that I can enter again and again through the same door and exit through the row of 6 other options 6 times..That would give me 6!*7! right? I don't mean to enter and exit only once.

- Mar 19th 2013, 06:16 PMSorobanRe: 7 doors
Hello, Paze!

Quote:

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?

Justyour way through it . . .*talk*

. . . . 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 . . .

- Mar 19th 2013, 06:36 PMPazeRe: 7 doors
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.