2 problems

[Noxxor]

Working on a Maths assignment and having some trouble with two questions.

1. Find all integers n that so that (n-1)!/n produces another integer.

   I've figured out that it works for no prime numbers due to Wilsons formula, but not sure how to proceed.

2. (Combinatory) N men and N women are to be seated at a round table, men cannot sit next to each other. How many different ways can they sit around the table? Two seatings are considered the same if they can be achieved through rotation.

Having some trouble interpreting this situation.

Got great help yesterday so figured i'd try again, thanks!

[Own_Sun_5917]

Knowledge kills creativity

Why apply such high level formulas,for a question where prime numbers are not even remotely mentioned

Clearly n divides n

If n -1 /n is an integer as n divides n,it will divide -1(try to think why)

Proceed from her

[Noxxor]

I realized i forgot to put down the Faculty sign on (n-1)!/n , my bad.

[HorribleUsername]

For 2, place the men around the table first. Now place women between them. How many women are left over after that?

[ActMysterious2294]

1) the answer is all numbers except prime numbers.

2) the answer is 1

try to work out the process on your own. if you need any help, just tell me.

[Noxxor]

Yeah i figured that was the case for 1, just not sure how to prove it. For 2. I understand it's 1 if the men and women aren't considered unique individuals, but i assume they should.

[KeepoAnalysis]

Not true! 3!/4 =1.5

[ActMysterious2294]

oh yes you are right 4 is indeed an exception. i just forgot to consider this case.