Explanation Definition: Fundamental counting principle: Suppose one event can occur in m ways and another event can occur in n ways, then the number of ways that both events can occur is formulated as m ⋅ n . It can be extended to three or more events. Permutation: A permutation is an arranged in the definite order of a number of objects will be taken in some or all at a time. The number of permutation of n different items takes from r items. The formula is, n P r = n ! ( n − r ) ! . Where, 0 < r ≤ n . Combination: The number of possible combination of r objects from a set of n objects. The formula is, n C r = n ! r ! ( n − r ) ! . Given: Customer: So what’s this new deal? Pizza chef: Two pizzas Customer [Toward four-year-old boy]: Two pizzas. Write that down. Pizza chef: And on the two pizza choose any toppings-up to five [ from a list of 11 toppings ]. Older boy: Do you… Pizza chef: …have to pick the same toppings on each pizza? No! Four-year-old-math whiz : Then the possibilities are endless. Customer: What do you mean? Five plus five are ten. Math whiz: Actually, there are 1, 048, 576 possibilities. Customer: Ten was just a ballpark figure. Old man: You go that right. Calculation: The person has to order a single pizza with 5 toppings out of 11. The boy can order a pizza with 0 toppings, 1 toppings, 2 toppings, 3 toppings, 4 toppings or 5 toppings. It can be calculate by using the combinations. Compute the number of possibility for one pizza orders. 11 C 0 + 11 C 1 + 11 C 2 + 11 C 3 + 11 C 4 + 11 C 5 = 1 + ( 11 ! 1 ! ( 11 − 1 ) ! ) + ( 11 ! 2 ! ( 11 − 2 ) ! ) + ( 11 ! 3 ! ( 11 − 3 ) ! ) + ( 11 ! 4 ! ( 11 − 4 ) ! ) + ( 11 ! 5 ! ( 11 − 5 ) ! )

13th Edition

ISBN: 9781285697734

Author: karl J. smith

Publisher: Cengage Learning US

See similar textbooks

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …

Videos

Question

Chapter 12.3, Problem 56PS

To determine

To find:

The number of possible different pizza orders.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 55PS

Chapter 12.3, Problem 57PS

Students have asked these similar questions

You may need to use the appropriate appendix table or technology to answer this question. You are given the following information obtained from a random sample of 4 observations. 24 48 31 57 You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 49. (Assume the population is normally distributed.) (a) State the null and the alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: (b) Determine the test statistic. (Round your answer to three decimal places.) (c) Determine the p-value, and at the 5% level of significance, test to determine whether or not the mean of the population is significantly different from 49. Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is insufficient evidence to conclude that the mean of the population is different from 49.Do not reject H0. There is sufficient evidence to conclude that the…

No chatgpt pls

Chapter 12 Solutions

Nature of Mathematics

Ch. 12.1 - IN YOUR OWN WORDS What is a permutation? What is...Ch. 12.1 - Prob. 2PS Ch. 12.1 - Prob. 3PS Ch. 12.1 - Prob. 4PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P2 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 9P4 Ch. 12.1 - Prob. 8PS Ch. 12.1 - Evaluate each expression in Problems 3-32. 52P3 Ch. 12.1 - Evaluate each expression in Problems 3-32. 4P4

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The number of possible different pizza orders.

Solution Summary: The author explains the fundamental counting principle of mcdot n, which can be extended to three or more events.

Concept explainers

Videos

To find: The number of possible different pizza orders.

Want to see the full answer?

Chapter 12 Solutions

To find:

The number of possible different pizza orders.