How many samples of size $4$ selected from $10$ red and $5$ white numbered marbles have exactly $3$ red marbles?

Question

I can't seem to wrap my head around permutation and combination.

For instance here is a very straight forward question:

10 red, 5 white, numbered marbles

How many samples (of size 4) have exactly 3 red marbles?

So what I'm thinking is 10 C 3 straight forward enough so far. However, I can't seem to understand why the answer is 10 C 3 $\cdot$ 5 C 1. I don't understand how to interpret the 5 C 1. (out of the 5 items we choose 1 ??)

Please help.

Answer 1

Next to the $3$ red marbles you also choose $1$ white one out of $5$.

There are $\binom51=5$ possibilities for that, because they are distinguishable (they have a number).