There is a group of 10 students consisting of 3 wearing red shirts and 7 wearing black shirts. Using combinatoric (combination and / permutation) notation, answer the following.

a) How many groups of 5 students could be formed wearing any colour shirts?

b) How many groups of 5 students could be formed where 3 students are wearing black shirts and 2 student is wearing red shirts?

c)If 5 of the 10 students are waiting in a queue to borrow a book at the library, how many ways could the queue be formed?

7. A researcher found that there is an increase in undergraduate students doing part- time jobs to partially support their expenses. It is assumed that 55% of UWindsor students do part time jobs in this current year. The researcher randomly selected 150 UWindsor students and checked whether they work part-time jobs. Answer the following based on this data:

   1. Find the probability that more than 90 students of these 150 selected said that they do part-time jobs.

   2. Find the probability that less than 80 students of these 150 selected said that they do part-time jobs.

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. The students studied were enrolled at a large Midwestern university several years ago. Discuss how you would conduct a similar study at a college or university of your choice today. Include a description of all the variables that you would collect for your study.

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. The students studied were enrolled at a large Midwestern university several years ago. Discuss how you would conduct a similar study at a college or university of your choice today. Include a description of all variables that you would collect for your study.

A set of hypothesis and a conclusion are given. Use the valid argument forms to deduce the conclusion from the hypothesis.

(i) p v q,

(ii) q ->r,

(iii)(p^s) ->t,

(iv) not r,

(v) (not q) -> (u ^ s)

(vi) t

Use the given transformation to evaluate the integral. (12x + 8y) dA R , where R is the parallelogram with vertices (−1, 3), (1, −3), (2, −2), and (0, 4) ; x = 1/ 4 (u + v), y = 1/ 4 (v − 3u)

Find the velocity, acceleration, and speed of a particle with the given position function.

r(t) =

9 cos(t), 8 sin(t)

Sketch the path of the particle and draw the velocity and acceleration vectors for

t =

.

The standard emf for the cell using the overall cell reaction below is +2.20 V:
2Al(s) + 3I₂(s) →→ 2AI³⁺(aq) + 6I^-(aq)
The emf generated by the cell when [AI³⁺] = 3.5 × 10^-3 M and [I^-] = 0.30 M is ________ V.

Which of the following systems (i.e. pair of metals) would you expect to exhibit complete solid solubility? Explain your answers. (i) Cr-V (ii) Mg-Zn (iii) Al-Zr (iv) Ag-Au (v) Pb-Pt

Let T be an operator on a finite-dimensional complex vector space V, and suppose that dim Null T = 3, dimNullT2 =6. Prove that T does not have a square root; i.e. there does not exist any S ∈ L (V) such that S2 = T.