In light of recent events, the most recent inventory shipment did not arrive at the Mystical Counting and Probability Emporium. Fortunately, our class is coming to the rescue to supply the store with our own magical goods! Each of us are bringing some number of fun objects (be as creative as you want!) for some (non-negative) price. For myself, I am bringing in $12$ (indistinguishable) metallic feathers from my pet Stymphalian bird, being sold for $9$ gold coins each. Lizzie is the first customer of the day. She brings with her $100$ gold coins. She can spend any amount of money between $0$ and $100$ gold coins, but she cannot spend more than that.
1) Calculate how many different ways Lizzie can spend money at the Emporium given the items that your other classmates have already added to or bought from the store room. For example, how many different combinations of Stympalian feathers Lizzie could buy. (Notice that she cannot buy all because gold coins!)