Task $9 / 67$ In a class, three students have the grade excellent in mathematics, twelve have the grade good, and the rest have satisfactory and sufficient. To promote the best students, the teacher assigns each of the excellent students a unique mathematical problem to solve; each of these students is to select four of the good students to work with.

How many ways are there to divide the twelve collaborators into groups of four for the three excellent students?
The first of the very good students has 12 options to choose the first employee, 11 options for the second, 10 for the third, and 9 for the fourth. Since the order of the employees does not matter, he has not $12 \cdot 11 \cdot 10 \cdot 9$ but only $\frac{12 \cdot 11 \cdot 10 \cdot 9}{1 \cdot 2 \cdot 3 \cdot 4}=495$ ways to choose his employees.

The second of the very good students has correspondingly $\frac{8 \cdot 7 \cdot 6 \cdot 5}{1 \cdot 2 \cdot 3 \cdot 4}=70$ ways, and the third must take the remainder.

In total, there are thus $495 \cdot 70=34650$ ways to distribute the twelve employees among the three very good students.