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.

On the first of each month, shelly runs a 5k race. she keeps track of her times to track her progress. her time in minutes is recorded in the table: jan 40.55 july 35.38 feb 41.51 aug 37.48 mar 42.01 sept 40.87 apr 38.76 oct 48.32 may 36.32 nov 41.59 june 34.28 dec 42.71 determine the difference between the mean of the data, including the outlier and excluding the outlier. round to the hundredths place. 39.98 39.22 0.76 1.21

The frequency table shows the results of a survey comparing the number of beach towels sold for full price and at a discount during each of the three summer months. the store owner converts the frequency table to a conditional relative frequency table by row. which value should he use for x? round to the nearest hundredth. 0.89 0.90 0.92 0.96

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24