Combinatorics exercise about sets of forks, knives, spoons. Problem statement:
At various yard sales, a woman has acquired five forks, of which no two are alike. The
same applies to her four knives and seven spoons. In how many different ways can
three place settings be chosen if each place setting consists of exactly one fork, one
knife, and one spoon? Assume that the arrangement of the place settings on the table is
unimportant.
So far I figured the following thing out:
Since we have to serve 3 sets, having the sets already, we would have $3!=6$ different ways of arranging the already created sets.
What would be the next thing to calculate to count how many times ONE set could be arranged?
The part I am struggling with is that each fork (and knive, spoon respectively) is distinct from one another, so I can't just use this theorem:

It would be nice if somebody would only give me a hint so I can still figure it myself (Dont just handwaive). Thank you!

You asked for a hint:
Hint: Pick a fork. Pick a knife to go with it and a spoon to go with it; repeat; repeat again. Then remember that (according to the problem statement) the order in which sets are chosen doesn't matter, so this process overcounts, and that must be corrected for.
