Question

A college offers 3 introductory courses in​ history, 2 in​ science, 1 in​ mathematics, 4 in​ philosophy, and 2 in English.

a. If a freshman takes one course in each area during her first​ semester, how many course selections are​ possible?

b. If a​ part-time student can afford to take only one introductory​ course, how many selections are​ possible?

Answer 1

Solution

Part (a)

One course in history can be any one of 3 courses available and hence there are 3 options.

One course in science can be any one of 2 courses available and hence there are 2 options.

One course in mathematics has to be the only one course available and hence there is just 1 option.

One course in philosophy can be any one of 4 courses available and hence there are 4 options.

One course in English can be any one of 2 courses available and hence there are 2 options.

Now, for every one option of any course, there are as many options as indicated above of each of the other courses. Thus, total number of course selections possible = 3 x 2 x 1 x 4 x 2 = 48 Answer 1

Part (b)

Here, the student is able to take only one course. Totally, (3 + 2 + 1 + 4 + 2 = 12) courses are available, of which the student can opt for any one in 12 ways.

Thus, total number of course selections possible = 12 Answer 2

DONE