# How many ways are there to arrange the characters in Permutation?

I need to find how many ways you can arrange the characters in Permutation with the $N$ appearing before all of the vowels but after the $P$. I understand that you can place the $N$ and $P$ $C(6,2)$ ways, but I'm not sure how to accommodate for the vowels. I could place the $N$, the $P$, and the vowels $(6,3)$ ways if the vowels were consecutive, but they can be in any order with any of the other letters mixed in. Any help/hints would be greatly appreciated.

First choose seven slots for $N,P$ and all the vowels. How many ways to do that? $P$ has to go in the first of those and $N$ in the second. How many ways to arrange the vowels in the remaining slots that you chose? How many ways to arrange the remaining consonants in the slots you didn't choose? Note that there are two $t$'s
Group 1: Permute the vowels $AEIOU$ $5!$ ways, then add $PN$ on front
Group 2: Separately permute the remaining consonants $RMTT$, $\frac {4!}{2!}$ ways
Interleave the two groups choosing $4$ from $11$, $\binom {11}{4}$