I have been thinking about a Rashba [Rav Shmuel Ben Aderet] in Kidushin page 17 for some time already. He asks from inheritance of a convert. He could not say to his brother "take the idols and I will take the other stuff," if inheritance of a convert was from the Torah. So we see "there is no choice" אין ברירה [going back in time.] But one brother can say to another, "You take the produce in one place, and I in another," and his idea is to get the produce which already has the tithes taken from it. The Rashba answers that there is choice in one sort of things, but not in two sorts. Then he asks from a gemara in Temura where you have two partners dividing up ten sheep against 9 and a dog. All the ten that are opposite to the set with the dog are considered the "price of a dog" and therefore can not be brought as sacrifices. The Gemara asks let one sheep be for the dog and the rest would be OK. So from that question we see there is choice even by two types. אפילו בשני מינים יש ברירה
Rav Shach suggests that even in dividing among inheritors there is some ambiguity if the act is as they are buyers, but the actual things they are dividing are thought to be simply inheritance. Or if in the objects themselves there is an ingredient of being buyers. So the Gemara that holds one brother could not say "Take the idols," holds they are buyers, but the other Gemara in Temura holds they are inheritors [in two types] and so the saying of ''take the idols" would not be forbidden except for the fact that he agrees to the existence of the idols which makes that act forbidden. [It would not be forbidden because of "no choice since we see in Temura that "there is choice"יש ברירה even by two sorts of things.]