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7. In how many ways can a committee of three be formed from a group of 10 members?

7. In how many ways can a committee of three be formed from a group of 10 members?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Exercises 4.3 Evaluate the following. 1. „C2 3. 15C10 5. C7 2. C. 4. C0 6. „Cn-r+1 Answer the following. 7. In how many ways can a committee of three be formed from a group of 10 members? 8. Ten points lie in a plane, no three of which are collinear. a) How many lines can be drawn using these points? b) How many triangles can be drawn using the vertices chosen from these points? 9. At MSA Academy Inc., a four-person committee is chosen from 15 teachers and a principal. In how many ways can the committee be formed if a) the principal must be in the committee? b) any four will be chosen from the group? c) the committee consists of teachers only? 10. From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can this be done? 11. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu? 12. 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? 13. 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? 14. A man is to walk from A to B along any of the paths shown. If he walks north or east, how many different routes can he take? A
Transcribed Image Text:Exercises 4.3 Evaluate the following. 1. „C2 3. 15C10 5. C7 2. C. 4. C0 6. „Cn-r+1 Answer the following. 7. In how many ways can a committee of three be formed from a group of 10 members? 8. Ten points lie in a plane, no three of which are collinear. a) How many lines can be drawn using these points? b) How many triangles can be drawn using the vertices chosen from these points? 9. At MSA Academy Inc., a four-person committee is chosen from 15 teachers and a principal. In how many ways can the committee be formed if a) the principal must be in the committee? b) any four will be chosen from the group? c) the committee consists of teachers only? 10. From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can this be done? 11. A chef can prepare 20 different dinners. In how many ways can he select 6 of them for today's menu? 12. 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? 13. 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? 14. A man is to walk from A to B along any of the paths shown. If he walks north or east, how many different routes can he take? A
15. 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 d) 4 females and 1 male b) 3 females and 2 males e) 5 females c) at least 3 females 16. How many 4-person committees are possible from a group of 10 people including Francis anc 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? A warehouse receives a shipment of 20 computers, of which five are defective. Eight computers are then randomly selected and then delivered to a store. a) In how many ways can the store receive no defective computer? b) In how many ways can the store receive three defective computers? c) In how many ways can the store receive all five defective computers? 18. Find the number of different poker hands that contain exactly 3 kings, while the other remaining 2 cards do not form a pair. 19. Find the number of full houses in a poker hand, that is, the number of poker hands with 3 of a kind and 2 of a kind. 20. A 5-card hand is dealt from a standard 52-card deck. a) How many such hands are possible? b) How many hands contain both a queen and a king? c) How many hands contain 3 face cards and an 8? d) How many hands contain only red cards?
Transcribed Image Text:15. 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 d) 4 females and 1 male b) 3 females and 2 males e) 5 females c) at least 3 females 16. How many 4-person committees are possible from a group of 10 people including Francis anc 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? A warehouse receives a shipment of 20 computers, of which five are defective. Eight computers are then randomly selected and then delivered to a store. a) In how many ways can the store receive no defective computer? b) In how many ways can the store receive three defective computers? c) In how many ways can the store receive all five defective computers? 18. Find the number of different poker hands that contain exactly 3 kings, while the other remaining 2 cards do not form a pair. 19. Find the number of full houses in a poker hand, that is, the number of poker hands with 3 of a kind and 2 of a kind. 20. A 5-card hand is dealt from a standard 52-card deck. a) How many such hands are possible? b) How many hands contain both a queen and a king? c) How many hands contain 3 face cards and an 8? d) How many hands contain only red cards?
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