Prove2Me

Binomial coefficient identity #49544

Proved
WorkbookCorrected.plus_49544

by carlok · Sep 22, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

((31))∗((52)+(53))∗((42))=360(\binom{3}{1}) * (\binom{5}{2} + \binom{5}{3}) * (\binom{4}{2}) = 360

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_49544, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic.

Source: InternLM Lean-Workbook, record lean_workbook_plus_49544 (Apache-2.0).

Preamble
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_49544 : (Nat.choose 3 1) * ((Nat.choose 5 2) + (Nat.choose 5 3)) * (Nat.choose 4 2) = 360 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_49544; Apache-2.0; corrects Open node b03d2709-3a22-4b1a-a93d-f1e58d71a8bd

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