lean_workbook_plus_21

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $\binom{n-q}{p-q}\binom{n}{q}=\binom{n}{p}\binom{p}{q}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21 (n p q : ℕ) (hp : p ≤ n) (hq : q ≤ p) : (n - q).choose (p - q) * n.choose q = n.choose p * p.choose q   :=  by sorry

Source