Mathematics & Probability
Section 1
Core Idea
Permutations count the number of ways to arrange items when order matters. Combinations count selections when order doesn't. The distinction sounds academic but carries enormous practical weight: the number of possible outcomes in any system — product configurations, hiring sequences, strategic choices — is usually far larger than intuition suggests. A team of 10 candidates for 3 roles has 720 permutations (order matters) but only 120 combinations (order doesn't). This combinatorial explosion explains why systems feel unmanageable as they scale, why testing every option is often impossible, and why structured approaches to narrowing possibilities matter more than exhaustive search. The model trains you to estimate the size of a decision space before entering it, and to recognize when the space is too large for brute-force analysis.
Free playbook
Get The Business Model Playbook
58 business models, one visual page each: how the money flows, the metrics that matter, and who runs it. Free when you join the Faster Than Normal email.
Free. No spam. Unsubscribe anytime.
Section 2
How to See It
Product
You're seeing it when your feature configuration allows users to set 8 binary toggles, creating 256 possible states. The QA team can't test every combination — they need a structured approach to coverage.
Hiring
You're seeing it when you're building a founding team and the order of hires matters: hiring an engineer first then a designer creates a different culture than the reverse. The permutations are distinct outcomes, not just different sequences.
Strategy
You're seeing it when a go-to-market plan involves choosing 3 channels from 12 options. The 220 possible combinations make it clear that intuition alone can't evaluate the full space — you need selection criteria.
Section 3
How to Use It
Before evaluating options, estimate how many combinations or permutations exist. If the number is manageable, evaluate systematically. If it's explosively large, use heuristics, constraints, or ranking criteria to prune the space first. Recognize when order matters (hiring sequence, launch sequence, negotiation moves) versus when it doesn't (feature selection, resource allocation). This distinction changes both the math and the strategy.
Decision filter
"How large is the decision space, and does the order of choices change the outcome?"
As a founder
When facing multi-variable decisions — team composition, feature bundles, market entry sequence — estimate the combinatorial space first. If it's large, define constraints to reduce it before analyzing options. Don't waste cycles on exhaustive evaluation when structured elimination gets you to a decision faster.
Section 5
Founders & Leaders
Jensen HuangFounder & CEO, NVIDIA
Huang built NVIDIA into a computing powerhouse by understanding combinatorial scale. GPU architecture is fundamentally a combinatorics problem: how to process massive parallel computations across thousands of cores simultaneously. Huang recognized that the explosion of possible data paths and processing configurations in parallel computing required architectural choices that constrained the combinatorial space intelligently rather than brute-forcing every possibility. The same thinking applied to NVIDIA's strategic positioning: instead of chasing every possible market (the full combinatorial set), Huang selected the specific combination of gaming, data centers, and AI that created compounding advantages. Founders face equivalent choices — the combinatorial space of markets, products, and channels is vast, and the winners constrain it deliberately.
Section 7
Connected Models
Reinforces
Exponential Growth
Combinatorial quantities grow exponentially as inputs increase. Understanding permutations and combinations reveals why small additions to a system's variables can create enormous increases in complexity.
Reinforces
Explore-exploit Tradeoff
When the combinatorial space is too large to explore fully, the explore-exploit tradeoff provides a strategy: sample enough combinations to build signal, then exploit the best ones rather than continuing to search.
Tension
Brute Force Solution
Brute force attempts to evaluate every option. Combinatorial explosion makes this impossible in most real-world decision spaces — forcing the shift from exhaustive evaluation to structured pruning.
Section 8
One Key Quote
— Blaise Pascal"The arithmetic of life is combination."
Section 11
Summary & Further Reading
Permutations count ordered arrangements; combinations count unordered selections. Together they quantify decision-space size. Estimate the combinatorial scale of any multi-variable decision before entering it, and use constraints to prune the space when it exceeds your capacity to evaluate exhaustively.
01
Book
Foundational text on counting principles and combinatorial methods.
02
Book
Strategic decision-making when the space of possible moves is combinatorially large.
03
Book
How computer science algorithms solve combinatorial problems humans face daily.