For questions about the study of finite or countable discrete structures, specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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Combinatorics problem involving n-dimensional space

Consider a set of more than $\frac {2^{n+1}} {n}$ points $(n>2)$, chosen from the $2^n$ points of the $n$-dimensional space which have the coordinates $\{ \pm1, \pm1, ..., \pm1 \}$. Show that ...
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Number of paths between two points in the first Quadrant.

[Extension of this] We can move in 4-directions and we need to reach $(0,b)$ from $(a,0)$ in exactly $n$ steps keeping in the first quadrant ($x\ge0$ and $y\ge0$) [$a,b\ge0$] Similar to previous ...