You've joined the CSCI Data Science team, and now you're in charge of how to distribute projects for students to work on in teams. The 4 projects are: Data Science, Machine Learning, Algorithmic Theory, and Computational Biology. There are 22 students on the team, each of which needs a project.
Please leave your answer unsimplified, in terms of multiplications, sums, powers and factorials. Do not leave the answer in terms of P(n, r) or C(n, r) notations.
(a) How many different ways can you allocate the 22 students to the projects?
(b) For Part (b) only, you realize that you want to make sure that each of the 4 teams has at least 3 students. Now how many different ways can you allocate the 22 students to the projects?
For each part, only count the ways to allocate numbers of students: putting 21 students on Data Science and 1 on Biology represents one way, not many. Each student should get a project.