Regarding the formula for binomial coefficients:
the professor described the formula as first choosing the $k$ objects from a group of $n$, where order matters, and then dividing by $k!$ to adjust for overcounting.
I understand the reasoning behind the numerator but don't understand why dividing by $k!$ is what's needed to adjust for overcounting. Can someone please help me understand how one arrives at $k!$? Thanks.