Fundamental Counting Principle
The fundamental counting principle states that if there are p ways to do one thing, and q ways to do another thing, then there are p × q ways to do both things.
Example 1:
Suppose you have 3 shirts (call them A, B, and C), and 4 pairs of pants (call them w, x, y, and z). Then you have
3 × 4 = 12
possible outfits:
Aw, Ax, Ay, Az
Bw, Bx, By, Bz
Cw, Cx, Cy, Cz
Example 2:
Suppose you roll a 6-sided die and draw a card from a deck of 52 cards. There are 6 possible outcomes on the die, and 52 possible outcomes from the deck of cards. So, there are a total of
6 × 52 = 312
possible outcomes of the experiment.
The counting principle can be extended to situations where you have more than 2 choices. For instance, if there are p ways to do one thing, q ways to a second thing, and r ways to do a third thing, then there are p × q × r ways to do all three things.
