If ${}^nP_{12}={}^nP_{10}×6$, than what is $n$? 
If ${}^nP_{12}={}^nP_{10}×6$, than what is $n$?

I am at year 11. I do understand the concept of $^nP_r,{}^nC_r$. Once I know the $n$ I can calculate. I got stuck on this.

So to compute nPr we do $n(n-1)\ldots(n-r+1)$. We note the following recurence
\begin{equation}
nPr = nP(r-1) \times (n-r+1)
\end{equation}
If you apply this recurrence twice, you should find a quadratic equation that $n$ must satisfy. When you find the solutions, pick the one such that both $nP12$ and $nP10$ make sense, and you can then verify that the solution is correct.
