Background
The coefficient of $x^ry^{n-r}$ is the number of terms with exactly $r$ $x$'s before grouping.
For example, $(x+y)^3=xxx+xxy+xyx+xyy+yxx+yxy+yyx+yyy=x^3+3x^2y+3xy^2+y^3.$
"#" = number.
Some proof of the binomial theorem claims that
#of terms with exactly $r$ $x$'s before grouping = #of $r$-subsets of $\{1,...,n\}$ = $C(n,r)$ or $n\choose r$
There is an implicit bijection such that the each subset corresponds to the position of the $x$'s.
My Question
What is an example of such a subset of an $r$-subset of $\{1,...,n\}$? Is this equivalent to saying $r$-element subset?
Thank you.