[Solution Library] In choosing a three-scoop sundae, you decide on one, two, or three flavors of ice cream; choose your ice cream from among ten varieties; choose
Question: In choosing a three-scoop sundae, you decide on one, two, or three flavors of ice cream; choose your ice cream from among ten varieties; choose from five choices of toppings; say yes or no to whipped cream, nuts, and a cherry.
- How many possibilities of ice cream scoops are there?
- Using the Difference Rule (Theorem 6.3.2), write an expression for the number of topping options.
- How is (b) related to the Power Set of the toppings?
- Find a formula for the size of the power set of a set with \(n\) elements and justify your answer. (Hint: can you think of a way to use binary numbers?)
- Use the previous parts to find out how many different sundaes are possible.
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