# March 30 Exercise (b) and (c) from lecture

Exercise: Complete parts (b) and (c) below for your team.

Team parentheses:
Let $C_n$ be the number of ways of parenthesizing a product of $n+1$ numbers.

Team binary rooted trees:
Let $C_n$ be the number of full, binary, rooted trees with $n+1$ leaves.

Team triangulated polygons:
Let $C_n$ be the number of ways of triangulating a polygon with $n+2$ sides.

(b) Find a recursive formula for $C_n$. (That is, find a formula for $C_n$ in terms of $C_0, C_1, C_2, \dots, C_{n-1}$.)

(c) Use your formula from (b) to determine $C_5$ and $C_6$.

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