Technical meaning of two alike combinatorial problems

Question

I am confused in how to interpret two alike combinatorial problems, because to me they both look the same. These are the problems:

1. How many ways are there to put $24$ distinguishable flags on $18$ distinguishable flagpoles?

The answer to this problem is $\binom{18+24-1}{24}24!$, so first is to arrange the flags as if they were indistinguishable and the arrange them in order.

2. How many ways are there to put 8 distinguishable balls into 10 distinguishable boxes?

The answer to this question is $10^8$.

If the first problem I consider it as distinguishable balls in distinguishable boxes, both problems should be the same, what's the catch then?

Answer 1

The order of the flags on each flagpole matters.

Once we have decided which objects go into which box, their order within the box does not matter.