(Give a combinatorial proof of each of the following identities. In other words, describe a collection of combinatorial objects and then explain two different methods for counting those objects. Leave each identity in the form given. Do not rearrange terms or use any other identity to simplify the equation.)
Prove that for n greater than or equal to 3,
n^3 - n = 6(nC3) + 6(nC2)
The Attempt at a Solution
This is my first Combinatorics class, and I must say that I don't think like this at all. It's all new to me and I don't understand anything in a combinatorial sense, but rather I understand things inductively and algebraically. Please give me a hint in how I could do this. I don't exactly want an answer, just a little help. Thank you so much for your time.