I am wondering whether the function $n \choose k$ is defined for $n \lt k$, or if we assume otherwise. If so, what would be the contexts in which we would want to compute $n \choose k$ where $n \lt k$?
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Your question seems to have already been answered here – Jiaze Zhang Sep 11 '23 at 09:19
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How would you define the factorial of a negative number, like $(-1)!$? – Dominique Sep 11 '23 at 09:19
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1For $n\in\mathbb{N}$ and $n<k$ $$\binom{n}{k}=0$$ – bob Sep 11 '23 at 09:19