# A Problem on Combinatorics

What is the cardinality of the set $\{(j_1,...,j_{m-2}): 2 \le j_1 <\ldots < j_{m-2} \le m\}$, where $m$ is some given positive integer (say, $100$ or $500$)?

You are choosing $m-2$ elements among the $m-1$ elements $2, 3, \dots, m$, so it's $$\dbinom{m-1}{m-2} = \dbinom{m-1}{1} = m - 1.$$ This is because your only choice is which one of the $m-1$ elements you are leaving out.