Concept explainers
A pizza parlor problem. How many different large pizzas with no double toppings can be made? (For example, mushroom, pepperoni, and sausage is one possibility, and so is mushroom and sausage, but not double mushroom and sausage. Your count should also include the case of no toppings.) You can’t answer the question yet because you don’t know how many toppings the pizza parlor offers.
a. Determine the number of different pizzas when there are exactly 3 toppings to choose from (e.g., mushroom, pepperoni, and sausage).
b. Determine the number of different pizzas when there are exactly 4 toppings to choose from.
c. Determine the number of different pizzas when there are exactly 5 toppings to choose from.
d. Look for a pattern in your answers in parts (a), (b), and (c). Based on the pattern you see, predict the number of different pizzas when there are lo toppings to choose from.
e. Now find a different way to determine the number ofdifferent pizzas when there are lo toppings to choosefrom. This time, think about the situation in the followingway: Pepperoni can be either on or off, mushrooms canbe either on or off, sausage can be either on or off, andso on, for all 10 toppings. Explain clearly how to use thisidea to answer the question and why this method is valid.
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
- Dance Committee A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 8 sophomores, 12 juniors, and 10 seniors are eligible to be on the committee, in how many ways can the committee be chosen?arrow_forwardDefective Units A shipment of 25 television sets contains three defective units. In how many ways can a vending company purchase four of these units and receive (a) all good units, (b) two good units, and (c) at least two good units?arrow_forwardIn Example 10, the team must consist of six boys and six girls. How many different 12-member teams are possible?arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage