Sterling numbers of the First kind Combinatorial Proof

[silvermane]

Homework Statement

Say we have sterling numbers of the first kind where we're given s(n, n-2) = 2(nC3) + 3(nC4)
for n greater than or equal to 4.

The Attempt at a Solution

So, for the left side, we have n people, and we wish to seat them at n-2 circular tables, where if we first seat n-2 people, we'll have 2 remaining people to sit down at any of the n-2 circular tables. I just want to know if I'm on the right track here; thank you so much for your time!

 

[pleasehelp328]

Hey, I was wondering if you figured out a solution to this and remember it? I can't figure it out at all!