4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu?5. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee is to select 3appetizers, 4 main courses, and 2 desserts. How many ways can this be done?6. One serving of banana split contains three scoops of different flavors of ice cream, 3 different syrups, 2 differenttypes of nuts, and with or without whipped cream. How many different ways can a banana split be made if thereare 12 ice cream flavors, 8 syrups, and 4 types of nuts to choose from?7. Suppose 6 female and 5 male applicants have been successfully screened for 5 positions. In how many ways canthe following compositions be selected? (a) 5 people regardless of sex. (b) 3 females and 2 males; (c) at least 3females; (d) 4 females and 1 male; (e) 5 females.8. How many 4-person committees are possible from a group of 10 people including Francis and Jojo if (a) there areno restrictions? (b) both Francis and Jojo must be in the committee? (c) either Francis or Jojo (but not both) mustbe in the committee?9. Awarehouse receives a shipment of 20 computers, of which five are defective. Eight computers are then randomlyselected and then delivered to a store. In how many ways can the store receive (a) no defective computer? (b)three defective computers? (c) all five defective computers?10. A 5-card hand is dealt from a standard 52-card deck. How many ways (a) such hands are possible? (b) contain botha queen and a king? (c) contain 3 face cards and an 8? (d) contain only red cards?2

4. Answer: In 38760 ways can he select 6 of them for today's menu out of 20.

Answered: 4. A chef can prepare 20 different…

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4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu?

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.CT: Chapter Test

Problem 2CT: A hospital cafeteria offers a fixed-price lunch consisting of a main course, a dessert, and a drink....

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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 the possible item groups or their sorting measures can be determined with counting principles.

Question

4. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu?
5. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet committee is to select 3
appetizers, 4 main courses, and 2 desserts. How many ways can this be done?
6. One serving of banana split contains three scoops of different flavors of ice cream, 3 different syrups, 2 different
types of nuts, and with or without whipped cream. How many different ways can a banana split be made if there
are 12 ice cream flavors, 8 syrups, and 4 types of nuts to choose from?
7. Suppose 6 female and 5 male applicants have been successfully screened for 5 positions. In how many ways can
the following compositions be selected? (a) 5 people regardless of sex. (b) 3 females and 2 males; (c) at least 3
females; (d) 4 females and 1 male; (e) 5 females.
8. How many 4-person committees are possible from a group of 10 people including Francis and Jojo if (a) there are
no restrictions? (b) both Francis and Jojo must be in the committee? (c) either Francis or Jojo (but not both) must
be in the committee?
9. Awarehouse receives a shipment of 20 computers, of which five are defective. Eight computers are then randomly
selected and then delivered to a store. In how many ways can the store receive (a) no defective computer? (b)
three defective computers? (c) all five defective computers?
10. A 5-card hand is dealt from a standard 52-card deck. How many ways (a) such hands are possible? (b) contain both
a queen and a king? (c) contain 3 face cards and an 8? (d) contain only red cards?
2

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