lean_workbook_plus_45195

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

So our answer is $\binom{20}{10}-11\binom{17}{10}+\binom{11}{2}\binom{14}{10}-\binom{11}{3}\binom{11}{10}=\boxed{24068}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_45195 :
  Nat.choose 20 10 - 11 * Nat.choose 17 10 + Nat.choose 11 2 * Nat.choose 14 10 - Nat.choose 11 3 * Nat.choose 11 10 = 24068   :=  by sorry

Cast the binomial coefficients to ℤ before evaluating the alternating inclusion-exclusion expression, whose integer value is24068.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Cast the binomial coefficients to ℤ before evaluating the alternating inclusion-exclusion expression, whose integer value is24068.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.