CombiBench

hackmath_1

How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students?

1716

https://www.hackmath.net/en/word-math-problems/combinatorics

hackmath

import Mathlib abbrev hackmath_1_solution : ℕ := sorry theorem hackmath_1 (sols : Finset (Fin 13 → Fin 2)) (h_sols : ∀ f, f ∈ sols ↔ ((List.ofFn f).count 0 = 6)) : sols.card = hackmath_1_solution := by sorry

hackmath_2

There are 8 athletes participating in a sprint competition. The referee needs to select 3 athletes and assign them specific rankings (first place, second place, and third place). How many different arrangements are possible?

336

https://www.hackmath.net/en/word-math-problems/combinatorics

hackmath

import Mathlib abbrev hackmath_2_solution : ℕ := sorry theorem hackmath_2 (sols : Finset (Fin 8 → Fin 4)) (h_sols : ∀ f, f ∈ sols ↔ ((List.ofFn f).count 0 = 1) ∧ ((List.ofFn f).count 1 = 1) ∧ ((List.ofFn f).count 2 = 1)) : sols.card = hackmath_2_solution := by sorry