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+---
+epic: 6
+story: 6.3
+title: "Factorial & Combinatorics"
+status: draft
+---
+
+## Epic 6 — Advanced Math & Functions
+**Goal:** Scientific, financial, and power-user math.
+
+### Story 6.3: Factorial & Combinatorics
+
+As a **CalcPad user**,
+I want to compute factorials, permutations, and combinations,
+So that I can solve probability, statistics, and combinatorics problems.
+
+**Acceptance Criteria:**
+
+**Given** the user writes `10!`
+**When** the engine evaluates
+**Then** the result is `3628800`
+
+**Given** the user writes `0!`
+**When** the engine evaluates
+**Then** the result is `1` (by mathematical convention)
+
+**Given** the user writes `nPr(10, 3)`
+**When** the engine evaluates
+**Then** the result is `720` (10! / 7!)
+
+**Given** the user writes `nCr(10, 3)`
+**When** the engine evaluates
+**Then** the result is `120` (10! / (3! * 7!))
+
+**Given** the user writes `100!`
+**When** the engine evaluates
+**Then** the result is computed using arbitrary precision arithmetic and is exact (not a floating-point approximation)
+**And** the full integer result is displayed (or a scrollable/expandable representation for very large numbers)
+
+**Given** the user writes `(-3)!`
+**When** the engine evaluates
+**Then** an error is displayed (factorial of negative integers is undefined)
+
+**Given** the user writes `3.5!`
+**When** the engine evaluates
+**Then** either the gamma function is used to compute `Gamma(4.5)` approximately `11.6317`, or an error indicates that only non-negative integer factorials are supported
+
+**Given** the user writes `nCr(5, 7)` where k > n
+**When** the engine evaluates
+**Then** the result is `0` (by combinatorial convention)