Contents
The Overall Picture
Theorem: The following are equal:
- The number of ways to pick n fruits from r types of fruit
- The number of monomials in r variables of degree n
- The number of arragnements of n "*"'s and r-1 "|"'s
- $ {n+r-1 \choose r-1} $
- The number of solutions to the equation $ x_1 + x_2 + \dots + x_r = n,\text{ where }x_i \in \mathbb{N} $
Choosing n fruits from r baskets
Example: ???
Stars and Bars
Example: ???
Kids and Chocolate
Example: ???
Driving Directions
Example: ???
