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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 $500$)?

Thanks a ton in advance!

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1 Answer 1

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.

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