Number of arrangements of the letters of the word "MISSISSIPPI" if all the S's and P's are separated.

Question

If the number of arrangements of the letters of the word "MISSISSIPPI" if all the S's and P's are separated is $K\cdot\dfrac{10!}{4!\cdot4!}$ then $K$ equals

My attempt is as follows:-

Assuming question is asking to separate all instances of S and all instances of P but S and P can be together

First arrange $M,I,I,I,I$, they can be arranged in $\dfrac{5!}{4!}=5$ ways

$5$ characters will give $6$ gaps, so choose any $4$ gaps out of $6$ and insert $S's$ over there $\implies \displaystyle{6\choose 4}$

Now we have $5\cdot\displaystyle{6\choose 4}$ arrangements containing $9$ characters and all $S's$ are separated. Now its time to push $P's$

$9$ characters will give $10$ gaps, so choose any $2$ gaps out of $10$ and insert $P's$ over there $\implies \displaystyle{10\choose 2}$

So total arrangements will be $5\displaystyle{6\choose 4}{10\choose 2}=5\cdot\dfrac{6!}{4!\cdot 2!}\cdot\dfrac{10!}{2!\cdot 8!}=\left(\dfrac{5\cdot 4!}{2!\cdot 2!\cdot 8\cdot7}\right)\dfrac{10!}{4!\cdot 4!}$

$$K=\dfrac{15}{28}$$, but actual answer is $K=1$

What mistake am I doing here?