Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:
Some beans are potatoes.
All carrots are potatoes.
All gourds are potatoes.

Conclusions:
I. Some gourds are beans.
II. Some carrots are gourds.
III. Some potatoes are gourds.