Their parents don't allow them _____ in the river because it's really dangerous.
swim
swimming
to swim
swam
本题考查 allow 的固定搭配。句意:他们的父母不允许他们在那条河里游泳,因为真的太危险了。根据 allow sb. to do sth. “允许某人做某事”的搭配可知答案为选项C。