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?