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Comments on Why 1. multiply the number of independent options? 2. add the number of exclusive options?

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Why 1. multiply the number of independent options? 2. add the number of exclusive options?

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Ironically, this textbook highlights understanding over memorization, but it doesn't expatiate the two WHY's in the question title!

When faced with a series of independent choices, one after the other, we multiply the number of options at each step. When faced with exclusive options (meaning we can't choose more than one), we add the number of options.

Make sure you see the difference. Don't memorize it — understand it.

David Patrick, BS Math & Computer Science, MS Math (Carnegie Mellon), PhD Math (MIT). Introduction to Counting & Probability (2005), p 29.

This multiplication is commonly pictured as a Tree Diagram, but Tree Diagrams don't expound it.

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1 comment thread

How have you tried to understand this and what kind of results has it given you thus far? (3 comments)
How have you tried to understand this and what kind of results has it given you thus far?
tommi‭ wrote about 2 years ago

How have you tried to understand this and what kind of results has it given you thus far?

DNB‭ wrote about 2 years ago

I have, but I haven't found an expatiation of multiplication vs. addition. Most books merely present the rule and expect you to memorize it.

tommi‭ wrote about 2 years ago

Okay, but have you done yourself to create the understanding? Have you calculated with some examples, created visual representations, etc. of relevant problems?