Using a combinatorial proof 
How should I solve this problem? can anyone help?
Thanks.

The expression on the left can been seen as choosing a committee of $k$ members out of $n$ people and then choosing a "president" from within the committee. 
Meanwhile, the expression on the right can be seen as first choosing a president out of $n$ people before choosing the rest ($k-1$ members) of the committee from the remaining $n-1$ people. 
Both count the same scenario so they are equal. (Remark: this is similar to the hint, changing the words "committee" and "president" to "subsets" and "elements" to use the hint given).
