In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

Explanation

The given word 'MISSISSIPPT' contains 11 letters, out of which there are 4 I's, 4 S's, 2 P's and 1 M.
Total number of words formed by the letters of the given word
`=(11!)/((4!)xx(4!)xx(2!))=34650.`
There are 4 I's in the given word and we treat IIII as 1 letter.
This single letter with remaining 7 letters will give us 8 letters out of which there are 4 S's, 2 P's, 1 M and 1 IIII.
So, the number of all such arrangements in which 4 I's are together
`=(8!)/((4!)xx(2!))=840.`
Thus, the number of words formed when 4 I's are together = 840.
Hence, the number of words formed when 4 I's are not together
`=(34650-840)=33810.`