What is the permutation of word "MISSISSIPPI"?

Question

What is the total no. of permutations of the letters of the word MISSISSIPPI in which no four "I"s come together?

My try-: $7!/4!\times 2! \times 8!/4!$

But not getting the right answer.

Please help

Answer 1

Number of permutations of the word MISSISSIPPI in which no $I$'s are together =Number of permutations of the word MISSISSIPPI-Number of permutations in which $4$ I's are always together

$\dfrac{11!}{4!2!4!}-\dfrac{8!}{2!4!}$

Answer 2

Just put all the i's together.

Total number of permutations =$\dfrac{11!}{4!2!4!}$. and total number of permutations in which all i's are together=$\dfrac{8!}{2!4!}$.

Just subtract and get the answer.

i.e$\dfrac{11!}{4!2!4!}-\dfrac{8!}{2!4!}$.