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2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committee be formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committee

2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committee be formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committee

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 36RE: In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president,...
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2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committee be formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committee consists of teachers only? 3. From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can this be done? 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
Transcribed Image Text:2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committee be formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committee consists of teachers only? 3. From a list of 40 teachers, 5 are to be promoted to subject area coordinator. In how many ways can this be done? 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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