Learn
The Fundamental Counting Principle is used when something happens in steps. Each step has a number of choices.
Rule:
If Step 1 can happen in a ways and Step 2 can happen in b ways, then:
Total = a · b
Key idea: If you’re choosing one thing AND then another thing, you usually multiply.
If you’re choosing this OR that, you usually add (that’s a different rule).
Examples
Example 1 (Outfits)
3 shirts and 2 pants.
3 · 2 = 6 outfits
Example 2 (Test-style code)
A code uses 1 letter (A–D) and 1 digit (0–9).
4 · 10 = 40 codes
Example 3 (3-step situation)
Choose 1 appetizer (5), 1 main (6), 1 drink (4).
5 · 6 · 4 = 120 meals
Practice
Try first. Then reveal the answer.
1.
A restaurant has 4 appetizers and 7 mains. How many meals can be made (one appetizer and one main)?
4 · 7 = 28
Because it’s appetizer AND main → multiply.
2.
A username is made with 1 letter (A–F) followed by 2 digits (0–9, digits can repeat).
How many usernames are possible?
6 · 10 · 10 = 600
6 letter choices, then 10 choices for each digit.
3.
A student chooses 1 hoodie (6 options), 1 shoe (3 options), and 1 hat (4 options).
How many outfits are possible?
6 · 3 · 4 = 72
Three steps → multiply all three.
Why this matters
This is the foundation of permutations and combinations. If students don’t understand this, they get destroyed later.