The Fundamental Counting Principle is used to find the number of possible outcomes of a combination of independent events.
Fundamental Counting Principle |
If an event $A$ has $m$ possible outcomes and an event $B$ has $n$ possible outcomes, then the total number of different outcomes for $A$ and $B$ combined is $m×n.$ |
For example, a store sells $2$ types of notebooks — with spiral binding and without. Each of these notebook types comes in $3$ different colors — blue, red, and green. According to the Fundamental Counting Principle, there are $2×3=6$ different notebooks to buy.
As mentioned above, this principle holds true only if the events are independent of each other. If the events are dependent, multiplying the number of possible outcomes for each event will not be correct. Considering the previous example, suppose that spiral bound notebooks came only in red.
There are still $2$ types of notebooks, and a total of $3$ colors for the non spiral bound notebooks. However, the possible number of notebooks to buy is not $2×3=6,$ but $4.$ This is because, in this case, the possible colors for a notebook depend on the type of notebook.