Selecting two identical boxes whose contents differ

If there are two ice cream boxes that are identical from the outside, in each of which a different kind of cake is stored, and in such a case the boxes are considered one mixture with each other, is it permitted to select between them, since the boxes are identical and are regarded as one type according to the opinion of the Rema? Or is it forbidden to select, because the different kinds inside the box define the boxes as two distinct types and it is considered a mixture of two types? And why is this different from the case of stuffed chicken discussed by the Taz, where seemingly what defines it as one type is that the stuffing is not part of the mixture itself — and apparently they are two types, and it is certainly no less than “large and small,” about which the Pri Megadim writes that even “large and small” are (considered) two types. This proves that it is not due to the difference between them, but rather because the stuffing is not mixed in, and we do not say that the stuffing is also part of the mixture. If so, then also with the boxes, the filling of the box should not affect the mixture so as to be considered two types?

Shalom u’vracha.

This is not one type, but two types, since a person cares whether he takes this one or that one.

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