📘 What is Combinatorics?
Combinatorics is the branch of math focused on counting and arranging objects. It helps answer questions like “how many ways can I choose 3 items from 10?”
Key Topics: permutations, combinations, partitions, pigeonhole principle.
In this calculator: you can compute the number of combinations C(n, k), also called “n choose k”, using the formula: C(n, k) = n! / (k!(n−k)!).
🎲 Combinatorics: n Choose k
Calculate the number of ways to choose k elements from n.
The Pascal Triangle is a recursive structure where each number is the sum of the two above it. It encodes combinations, binomial coefficients, modular symmetry, and harmonic patterns across arithmetic.
In modular reductions (like mod 2), it forms fractals such as the Sierpinski Triangle. In higher moduli, it reveals wave-like harmonic color cycles.