AI Tutor
Back to Combinatorial Proofs

Exercise 9

Avg difficulty 2.5

Establish the identity below using a combinatorial proof. (22)(n2)+(32)(n−12)+(42)(n−22)+⋯+(n2)(22)=(n+35).{2 \choose 2}{n \choose 2} + {3 \choose 2}{n-1 \choose 2} + {4\choose 2}{n-2 \choose 2} + \cdots + {n\choose 2}{2\choose 2} = {n+3 \choose 5}.

Hammond, Discrete Math for Shockers, §5.3 Combinatorial Proofs, Exercise 9

AI Tutor

Adapted from Discrete Math for Shockers © 2021 John Hammond. Licensed under CC BY-SA 4.0. Source: Discrete Math for Shockers. Imported at revision 2538beb.