Why doesn't the multiplication rule work here? I have the following question:

How many ways are there to select $3$ candidates from $8$ equally
qualified recent graduates for openings in an accounting firm?

I was given the following solution to it: $\binom{8}{3}$, however, I got the answer: $8 \times 7 \times 6$ by doing the multiplication rule, I was wondering why my answer doesn't work.
My initial reason is that in the multiplication rule there is the underlying assumption that order matters and here obviously order doesn't matter. However, I am posting this here as that is the first time I come to such a realization and I am not sure that my reasoning is correct, especially since that I never learned multiplication rule with the idea of order in my mind. Any clarification would be appreciated.

$\binom{8}{3}$ is the same as $\frac{8!}{3!5!}$ which is $\frac{8.7.6}{3!}$, so you just need to divide by the extra $3!$
That's because you have overlapping choices by e.g choosing ABC, is the same as ACB,BAC,BCA,CAB and CBA, 6 ways to get the same ABC.
