# Double Check Probability for Permutation

I have to find the sample space and a few probabilities here and I am wondering about if I am going down the right track for these. If I am incorrect, then please point me in the right direction, but not give me the full process.

There are 5 students that must finish 6 problems. Each problem is only worked on by one student. A teacher assigns each student to each problem.

Find the Sample Space: Total of $5^6$ ways to assign problems. Any 5 students can do each of the problems, hence $5^6$ ways.