A student entering a doctoral program in educational psychology is required to select two courses from the list of courses provided as part of his or her program.(a) List all possible two-course selections.(b) Comment on the likelihood thatEPR 602 and EPR 684EPR 602 and EPR 684 will be selected. EPR 622 EDUCATIONAL RESEARCH PLANNING AND INTERPRETATIONEPR 664 NONPARAMETRIC STATISTICEPR 602 INTERPRETIVE METHODS IN EDUCATIONAL RESEARCHEPR 652 THEORY OF MEASUREMENTSEPR 684 RESEARCH IN CHILD DEVELOPMENT

We need to list out all the possible two-course selections from the list of 5 available courses. Selecting 2 courses out of 5 means: forming combinations of 2 courses out of 5 courses. So using combinations we can calculate how many selections will be possible. This would be equal to 5C2. The formula of combinations is:

[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

For, for our case, the formula will be:

[tex]^{5}C_{2}=\frac{5!}{2!(5-2)!}=10[/tex]

This means, 10 possible two-course selections are possible. These selections are listed below:

EPR 622 and EPR 664
EPR 622 and EPR 602
EPR 622 and EPR 652
EPR 622 and EPR 684
EPR 664 and EPR 602
EPR 664 and EPR 652
EPR 664 and EPR 684
EPR 602 and EPR 652
EPR 602 and EPR 684
EPR 652 and EPR 684

This is the list of all possible two-course selections from the available 5 courses.

Part b) Likelihood that EPR 602 and EPR 684 will be selected

From the above list we can observe that there are total 10 possible options to select from and only one way of selecting EPR 602 and EPR 684.

Likelihood or Probability is defined as ratio of desired outcomes to total possible number of outcomes. So, desired outcome is 1 i.e. selecting EPR 602 and EPR 684, while, total possible outcomes are all the possible 2 course selections which are listed above. Hence, total number of possible outcomes is 10.

Therefore, likelihood of selecting EPR 602 and EPR 684 is = [tex]\frac{1}{10}=0.1[/tex]