Given $n,k$ how to find $r,s$ s.t. $r \neq n , s \neq k$ where $\binom {n}{k}=\binom{r}{s}$
from https://en.wikipedia.org/wiki/Combination all I have been able to find is $\binom {n}{k}=\binom {n}{n-k}$
Edit adding some context I pondered about this problem when I wondered if given 2 out of $n,k,c$ for $\binom {n}{k}=c$ one might be able to determine the other 2, but the identity $\binom {n}{k}=\binom {n}{n-k}$ clearly shows that there will be at least 2 values for k that would satisfy that equation, replacing the the factorial with gamme function , I wondered if the $\binom {n}{k}$ can have an inverse function (which of course it cant as it is not a bijection). So trying to find at least the families of the solutions that would satisfy the $\binom {n}{k}=c$ where $c$ is given and $n,k$ that satisfy the equation are by some generating expression of root values.