A school organization consists of 5 teachers, 7 parents and 6 students. A subcommittee of this group is formed by choosing 2 teachers, 3 parents and 3 students. How many different subcommittees can be formed?
We can break this problem into three parts.  First, we will count the number of ways to choose teachers for the subcommittee.  We need to choose 2 teachers from the 5 in the school organization, which gives $\dbinom{5}{2}=10$ ways to choose the teachers.  Next, we choose parents.  We need to choose 3 parents out of 7, which gives $\dbinom{7}{3}=35$ ways to choose the parents.  Finally, we choose the students.  There are 3 students chosen from 6, which gives $\dbinom{6}{3}=20$ ways to choose the students.  Each of these selections is independent, so the total number of possible subcommittees will be $10\cdot 35\cdot 20=\boxed{7000}$.