5.0 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
What combinatorial notation corresponds to the highlighted square?
!
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
What combinatorial concept corresponds to the highlighted square?
!
Back: The multiplicative principle.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
Which square corresponds to notation n^k?
!
Back:
!
END%%
%%ANKI
Basic
What combinatorial notation corresponds to the highlighted square?
!
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
What combinatorial concept corresponds to the highlighted square?
!
Back: k-permutations (falling factorials)
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
Which square corresponds to notation (n)_k?
!
Back:
!
END%%
%%ANKI
Basic
What combinatorial notation corresponds to the highlighted square?
!
Back: \binom{n + k}{k}
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
What combinatorial concept corresponds to the highlighted square?
!
Back: 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
Which square corresponds to notation \binom{n + k}{k}?
!
Back:
!
END%%
%%ANKI
Basic
What combinatorial notation corresponds to the highlighted square?
!
Back: \binom{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
What combinatorial concept corresponds to the highlighted square?
!
Back: Combinations
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
Which square corresponds to notation \binom{n}{k}?
!
Back:
!
END%%
Bibliography
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.