statistics and probabitity

Question

Next year, you will be taking three college courses, English 101, Math 101, and History 102. 

The English course is taught by Mr. Jefferies and Mrs. Adams. The Math course is taught by Dr. Garmin, Mr. Hancock, and Miss Star. The History course is taught by Dr. Fynstein and Ms. Rogers. 

On a sheet of paper, neatly draw a tree diagram to determine the sample space of the different ways you could take the courses based on the teachers. Below the diagram list the sample space. Use the first initial of the last name of each teacher. 

Answer 1

There are 2 x 3 x 2 = 12 ways the courses can be taken based on teacher.

For each of the 2 possibilities for English 101 there are 3 possibilities for Math 101 and for each combination of those 2 classes there are 2 possibilities for History 102.

The sample space, which is the collection of all distinct outcomes of the event based on teachers' first initials, is (English, Math, History):

(JGF, JGR, JHF, JHR, JSF, JSR, AGF, AGR, AHF, AHR, ASF, ASR).

The tree will have 2 branches for English 101, each of those have 3 branches for Math 101 and each of those have 2 branches for History 102.