notebook/notes/combinatorics/index.md

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title TARGET DECK FILE TAGS tags
Combinatorics Obsidian::STEM combinatorics set
combinatorics
set

Overview

When selecting objects, we can use the given table to hint at what counting strategy we should use:

Order Repeats Answer Shape Reference
Yes Yes n^k -
Yes No (n)_k permutations#Falling Factorials
No Yes \binom{n + k}{k} combinations#Stars and Bars
No No \binom{n}{k} combinations

%%ANKI Basic What does it mean for order to matter? Back: We get different outcomes if the same objects are selected in different orders. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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%%ANKI Basic What does it mean for repeats to be allowed? Back: The same object can be selected multiple times. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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%%ANKI Basic If order matters and repeats are allowed, the number of selections is usually formatted in what way? Back: n^k Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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%%ANKI Basic If order matters and repeats are disallowed, the number of selections is usually formatted in what way? Back: (n)_k (falling factorial) Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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%%ANKI Basic If order does not matter and repeats are allowed, the number of selections is usually formatted in what way? Back: \binom{n + k}{k} (stars and bars) Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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%%ANKI Basic If order does not matter and repeats are disallowed, the number of selections is usually formatted in what way? Back: \binom{n}{k} (combinations) Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.

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References