University Discrete Math Counting Techniques — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 2 definitions and 8 theorems, 6 worked examples, 2 diagrams, in 14 printable pages. This page lists what the notes cover. The notes themselves come with the University Discrete Math bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Counting Techniques — what the notes cover
7 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
The sum and product rules
- Theorem — The sum, product and complement rules
Also in this section: 1 worked example, 1 note on method and common errors.
The pigeonhole principle
- Theorem — The pigeonhole principle
Also in this section: 1 worked example, 1 note on method and common errors.
Permutations
- Definition — Factorials and permutations
- Theorem — Arrangements under a restriction
Also in this section: 1 worked example, 1 note on method and common errors.
Combinations
- Definition — Combinations
- Theorem — The division rule
Also in this section: 1 worked example, 1 note on method and common errors.
The binomial theorem and Pascal's identity
- Theorem — The binomial theorem
- Theorem — Pascal's identity and the symmetry rule
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Permutations and combinations with repetition
- Theorem — Arrangements of objects that repeat
- Theorem — Selections with repetition
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Where the notes are
The notes are one of the documents in the University Discrete Math Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Counting Techniques practice worksheet is free and stays free.
Every University Discrete Math topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Discrete Math units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Counting Techniques practice worksheet About the Counting Techniques unit test