In how many distinguishable ways can the yogurts be stored in the box? I'm not the best with probability and would to know if my thinking is right with this question.
A wooden box has $12$ compartments in which to store yogurts. In each compartment, there is room for one yogurt only. Suppose that $7$ yogurts are to be stored in the box, $4$ of which are Natural Yogurts (therefore indistinguishable from one another), and $3$ of which are Flavoured Yogurts ($1$ peach, $1$ banana, and $1$ passion fruit). In how many different ways can the yogurts be stored in the box?
I was thinking the answer might be $12P7/4!$ as there are $12$ compartments to choose from and there are $4$ indistinguishable flavours that would yield the same permutation.

We can choose $4$ indistinguishable slots in $C(12, 4)$ ways . For each of this the remaining $3$ distinguishable slots can be chosen in $C(8,3)*3!$ ways.So, we have $C(12,4)*C(8,3)*3!$ ways to choose
