Product Rule for Counting/Examples/Choices from 2 and 3

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Example of Use of Product Rule for Counting

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


Sources