There are $2$ white balls, $3$ red balls, and $1$ yellow ball in a jar. How many different ways are there to retrieve $3$ balls?
How many different ways are there to make a payment of $n$ dollars using any number of $\$1$ and $\$2$ bills?
Find the number of integer solutions to the equation $a+b+c=6$ where $-1 \le a < 2$ and $1\le b,\ c\le 4$.
For every integer $n$ from $0$ to $6$, we have $3$ identical weights with weight $2^n$ grams. How many total ways are there to form a total weight of $263$ grams using only these weights?