In how many of distinct permutations of the letters in the word MISSISSIPPI do the 4 I's not some together?

Explanation

The given word has 11 letters out of which there are four I's, four S's, two P's and one M.
`therefore` total number of permutations `=(11!)/(4!4!2!)`
Now consider four I's as one letter and 7 other which are four S's two P's and one M. So the number of permutations in which four I's are together `=(8!)/(4!xx2!)`
`therefore` the number of permutations in which the four I's do not come together
`(11!)/(4!4!2!)-(8!)/(4!xx2!)=(11.10.9.8.7.6.5)/((24)(2))-(8.7.6.5)/(2)`
`= 34650-840 = 33810`