jmc

First we count the arrangements if all the letters are unique, which is $11!$. Then since the I's, S's and the P's are not unique, we divide by $4!$, $4!$, and $2!$ for the arrangements of I's, S's, and P's, for an answer of $\frac{11!}{4!\times 4!\times 2!}=\boxed{34,650}$.