While reviewing a lesson on union and intersection, Mrs. Putnam again asked for three students to each write down a set of numbers from {1,2,3,4,5,6,7,8,9,10}. After they had done so, she looked at their sets and told the class, "Like last time, the union of these three sets is all ten numbers, but their intersection is empty."

One student interjected to say that he saw that two of the sets have a union that was all ten numbers.

Another student noted that there were two sets whose intersection was empty.

How many triplets of sets A, B, C satisfy all the above criteria?