3.0 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Combinatorics | Obsidian::STEM | 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.
END%%
%%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.
END%%
%%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.
END%%
%%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.
END%%
%%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.
END%%
%%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.
END%%
References
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.