# Questions tagged [factorial]

Questions on the factorial function, $n!=n\cdot(n-1)\cdot...\cdot1$. Consider using the tag (gamma-function) if dealing with noninteger arguments.

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### How many ways are there for 5 men and 11 women to stand in a line where there are at least 2 men in a row? [closed]

I have a question from a textbook that I could not really understand what's going on. The question goes like this: How many ways are there for 5 men and 11 women to stand in a line where there are at ...
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### Prove that (n!+1) is not divisible by any natural number between 2 and n. [closed]

I tried this question solving by mathematical induction. But no luck Is there is any easy way to prove that?
### A question about $\ln (kc-1)! \sim \ln(c!(c-1)! \dots(c-k)!) + c \cdot\alpha$?
Question I was recently fiddling with some math that me wonder if there was nice asymptotic equation of the form $k<c$: $$\ln (kc-1)! \sim \ln(c!(c-1)! \dots(c-k)!) + c \cdot\alpha$$ where $c$ is ...
### Is there a closed form of $\sum_{n=0}^{\infty} \frac{(-1)^n}{(4n+1)!!}$?
This may be an impossible problem. But I imagine it's worth asking still. What is the closed form of the sum: $$\sum_{n=0}^{\infty} \frac{(-1)^n}{(4n+1)!!}$$ Perhaps there isn't a closed form. ...