Assume that we have 10 marshmallows, 80 bananas, and 50 peaches. Your task is to first put 3 marshmallows on a stick, then 2 bananas, and finally 4 peaches. In how many ways can you make this stick?
Is this the correct solution to this particular problem? $\frac{9!}{4! 3! 2!}$
I would claim that if marshmallows etc. are indistinugishable, there is $1$ way because you are given a specific order the things must be in. If they are distinguishable, there are $10 \cdot 9 \cdot 8\cdot 80\cdot 79 \cdot 50 \cdot 49 \cdot 48 \cdot 47$ ways.