Astudent must take one physics, one chemistry, and one mathematics course during their junior year of high school. there are three courses to choose from for physics (p1, p2, p3), two courses to choose from for chemistry (c1, c2), and two courses to choose from for mathematics (m1, m2). how many possible combinations are there for the three physics, chemistry, and mathematics courses a student could select?

I'll write out one list of possible combinations as an example. Suppose we're looking at all paths following a choice of P1. Then we have:
P1 C1 M1
P1 C1 M2
P1 C2 M1
P1 C2 M2

So there are 4 possible choices with P1. Since there are 3 choices of P, there are 3*4 total combinations, or 12. In general, you can multiply the number of possibilities together to see how many total combinations can occur, I just wanted to illustrate why that works.