Medium Practice — Set 2

Quick Recap — Selection Problems

• Committees/teams: multiply independent choices $^aC_r\cdot{}^bC_s$; ``at least one'' via $2^n-1$ or complement.
• Geometry: from $n$ points (no 3 collinear) lines $=^nC_2$, triangles $=^nC_3$; a polygon's diagonals $=^nC_2-n$.
• Distributing identical objects into boxes: stars and bars, $^{n+r-1}C_{r-1}$.
• $^nC_r$ is largest near $r=\tfrac n2$.