To add a little explanation. Notice that the correct answer is 3 times the answer you got. That is becuase you chose to have the professor assign 2 projects to student A, then two projects to student B then the remaining 3 to Student C.
But there are two other ways the professor can assign the projects:
First 3 to Student A, then 2 to Student B then the remaining 2 to student C
and
First 2 to student A then 3 to student B and the remaining 2 to student C.
This gives us the 3 equations to add together.
7C2 * 5C2 *3C3
7C3 * 4C2 *2C2
7C2 * 5C3 * 2C2
Each one of them gives 210 combinations for a total of630 combinations.
-Carrie
