COUNTING_LOGIC
Permutations (nPr)
Ordering matters. How many ways to arrange objects in a specific sequence.
P(n, r) = n! / (n - r)!Combinations (nCr)
Ordering doesn't matter. Choosing subsets from a larger group.
C(n, r) = n! / [r!(n - r)!]PASCAL'S_TRIANGLE
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
"Infinite binomial expansion hidden in patterns."
TOOLS_KIT
Factorial Logic
Calculating permutations of large sets.
Pigeonhole Principle
Foundational existence proof tool.
Inclusion-Exclusion
Counting without double counting.
Catalan Numbers
Recursive binary tree structures.