confusion about # of ways and probability

[mehrasa]

In how many ways can you sit 8 people on a bench if 3 of them must sit together?

for this Q i can understand that we can consider those three ppl as one person then the answer is 6!*3!=4320

however, most time i will be confused when we need to divide total ways by the number of position for instance 8!/3!...i learned that when we have indistinguishable objects in the set wee need to divide by the # of those objects.....plz explain when we use multiplication, when we have to use division..

[gmatboost]

The people in this case are not indistinguishable, they are just sitting together.

If you are asked to arrange the letters in the word MISSISSIPPI, you would have to use division to account for the letters that are exactly the same and therefore do not create new arrangements: 11!/(4!4!2!).