combinatorics - An application of this binomical identity $binom{n}{k}=binom{n-1}{k}+binom{n-1}{k-1}$

I need a clarification on this manner, in terms of "When do I apply this form of

identity". I managed to proove it algebraically and combinatorially, using

"Pascal's triangle". so a proof is not needed. However I am not comprehending what it's

application in terms of combinatoric(or any) exersice.

$$\binom{n}{k}=\binom{n-1}{k}+\binom{n-1}{k-1}$$