Too many S's!

The number of ways we can arrange the 7 letters in the word "MISSISSIPPI", which are not "S" (1 "M", 4 "I"s and 2 "P"s):

$\frac {7!}{4!2!} = 105$

Now, we can put the each of 4 letter "S"s one by one in 8 places: after one of the other 7 letters or in the front. The number of ways this can be done is:

${ 8 \choose 4 } = 70$

Hence, our answer should be:

$105 × 70 = \boxed {7350}$