Social promotion distributions

It is the end of the school year, and a teacher is giving out awards to her 3 students. She has 6 distinct awards (for grades, attendance, generosity, etc.) to give out, and she will give each award to the student who is most deserving.

However, she knows that her students can be rather immature, and one of them might throw a fit if he or she doesn't get an award. She secretly decides to make sure that each student gets at least one award (even if he or she doesn't deserve it).

How many ways can the awards be distributed among the students if all of the awards are given?

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