Discrete Math › Section D · Counting › Topic D.1
Pascal's triangle and the binomial theorem
One triangle of numbers, built by nothing more than addition, answers a surprising range of counting questions: grid paths, strings of 0s and 1s, subsets, and the coefficients you get when you expand a power of a binomial.
In this topic
- A triangle built by addition
- Naming the entries
- Counting grid paths
- Bit strings and subsets
- Worked example: paths across a city grid
- The binomial theorem
- Worked example: a coefficient with a negative term
- Row sums and patterns
- A link to probability
- Common mistakes to avoid
- Key takeaways
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