Proving Pascal's Rule : $\binom n k =\binom{n−1}{ k−1}+\binom{n−1} k $ I have taken the R.H.S and used the combination formula $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
then I don't know other steps to solve it.

Here is a procedure to choose $k$ things from $n$ things. It is well known that there are $\binom{n}{k}$ ways to do this.
Pick the first item. It is either used or not.


*

*if it is used, we must pick $k-1$ things from $n-1$ remaining things, which we can do in $\binom{n-1}{k-1}$ ways

*it is is not used, we must pick all $k$ things from $n-1$ remaining things, which we can do in $\binom{n-1}{k}$ ways


Can you complete the argument?
