What is committee forming argument, and how do i use it on this?

I don't know what the committee forming argument is.

However proving this should be easy enough using the definition

$k \dbinom{n}{k} = k \dfrac{n!}{k!(n-k)!} = \\ \dfrac{n!}{(k-1)!(n-k)!} = \\ n \dfrac{(n-1)!}{(k-1)!((n-1)-(k-1))!} = \\ n\dbinom{n-1}{k-1}$

Thanks for your reply. However, i have already done it with algebra, so i already know how to do it the way you are doing. I need help on doing it specifically with a committee forming argument. I am stuck on how to start. Hints please? Also, can any mod take the check mark off??

Thank you very much! :)