[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.

  1. How many possibilities of ice cream scoops are there?
  2. Using the Difference Rule (Theorem 6.3.2), write an expression for the number of topping options.
  3. How is (b) related to the Power Set of the toppings?
  4. 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?)
  5. Use the previous parts to find out how many different sundaes are possible.

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