Algebra 2 / Unit 9: Probability
9.1 The Fundamental Counting Principle
Notes
If one choice can be made $m$ ways and a second choice $n$ ways, the two together can be made $m \cdot n$ ways.
- Multiply the number of options for each step.
- Watch for repetition: if items can't repeat, each step has one fewer option.
- Example: a 3-digit code with digits 0-9 has $10 \cdot 10 \cdot 10 = 1000$ options with repeats, but $10 \cdot 9 \cdot 8 = 720$ without.
Practice
You have 4 shirts, 3 pairs of pants and 2 pairs of shoes. How many outfits can you make?
$4 \cdot 3 \cdot 2 = 24$.
A license plate has 3 letters followed by 3 digits, and repeats are allowed. How many plates are possible?
$26^3 \cdot 10^3 = 17576 \cdot 1000$.
How many 4-digit PINs use the digits 0-9 with no digit repeated?
$10 \cdot 9 \cdot 8 \cdot 7 = 5040$.
Ready for more? Take the Unit 9 test.