## Bijective counting

1. Let $S = {1,2,...,n}$. How many ordered pairs $(A,B)$ of subsets of $S$ are there that satisfy $A \subseteq B$ ?

2. Let $S = {1,2,...,n}$. How many ordered pairs $(A,B)$ of subsets of $S$ are there such that $A$ and $B$ are disjoint ?

3. Consider a convex polygon on $n$ points such that no three points are collinear. A chord is a line segment between two non-adjacent vertices. If all chords are drawn, in how many interior points do they intersect ? Assume no three chords intersect at the same point.

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