Pls answer items no. 2, 3, 4, 5, 6, 7 and 8 thank u Exercise #3 (Portfolio)Answer the following.1. In how many ways can a committee of three be formed from a group of 10 members?2. At SSC, a four-person committee is chosen from 15 teachers and a dean. In how many ways can the committeebe formed if (a) the dean must be in the committee? (b) any four will be chosen from the group? (c) the committeeconsists 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 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?

Note: As per bartleby guidelines for more than one questions asked, only one question with three…

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?

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?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Pls answer items no. 2, 3, 4, 5, 6, 7 and 8 thank u

Exercise #3 (Portfolio)
Answer the following.
1. In how many ways can a committee of three be formed from a group of 10 members?
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?

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