Product Rule for Counting/Examples
Jump to navigation
Jump to search
Examples of Use of Product Rule for Counting
Choices from $2$ and $3$
The canonical example concerns choices from the menu at a restaurant:
You may select exactly one dish from each category:
- Starters
- $(1): \quad$ Crottled Greeps
- $(2): \quad$ Stone Soup
- $(3): \quad$ Petty-Dwarf Roots
- Main Course
- $(1): \quad$ Hufu Salad
- $(2): \quad$ Braised Trake in Funistrada
The diner then has $2 \times 3 = 6$ possible different meals:
- $(1): \quad$ Crottled Greeps with Hufu Salad
- $(2): \quad$ Crottled Greeps with Braised Trake in Funistrada
- $(3): \quad$ Stone Soup with Hufu Salad
- $(4): \quad$ Stone Soup with Braised Trake in Funistrada
- $(5): \quad$ Petty-Dwarf Roots with Hufu Salad
- $(6): \quad$ Petty-Dwarf Roots with Braised Trake in Funistrada
Choices from $4$, $3$ and $2$
Let $N$ be the number of ways you can choose at least $1$ item of fruit from:
- $4$ (indistinguishable) oranges
- $3$ (indistinguishable) bananas
- $2$ (indistinguishable) apples
Then:
- $N = 59$
Choices from $5$ and $3$
There are:
- $5$ different ways to travel from $A$ to $B$
- $3$ different ways to travel from $B$ to $C$.
Hence there are $5 \times 3 = 15$ different ways to travel from $A$ to $C$.
$6$ Football Matches
Let it be understood that a football match between two teams $\text A$ and $\text B$ can end as:
- A win for team $\text A$
- A draw
- A loss for team $\text A$.
That being understood, then there are $729$ ways to predict the results of $6$ football matches.