7. A regional committee has 5 members from Town A, 3 members from Town B, and 2 members from Town C. Ifwe wanted to choose a committee of 4 members, how many would have at least 2 members from Town A?8. Someone rolls a fair die twice. Let A be the event that the first roll is 6, and B be the event that the sum of bothrolls is greater than ten. Find the values of P(A), P(B), P(B|A), and P(A n B). Based on theses computations,are these events independent? Support your computations with a conceptual explanation as to why this is thecase.9. Let A, B, and Cbe three events that are all independent of each other and P(A) = P(B) = P(C) =the value of P(A UBUC)?What is%3D%3!

HERE AS PER GUIDELINES I HAVE CALCULATED 1ST MAIN QUESTION here use combination

Answered: 7. A regional committee has 5 members…

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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f) Student council needs to create a committee of 6 students to run their social events. 12 students applied to be on the committee, 8 women and 4 men. The committee must have at least 1 woman and at least 1 man. How many ways can the committee be selected?
3. Out of 100 Californian children that had a dental exam, 75 had cavities. Of the 80 Northern Californian children that had a dental exam, 60 had cavities. a. How many Southern Californian children had cavities? b. How many Southern California Children did not have cavities?
4. When the merchants in the annual Math Department Parade lined up 4 abreast, there was 1 odd person, when they tried 5 in a line, there were 2 left over; and when 7 abreast, there were 3 left over. How large is the Department?
2. An emergency committee consisting of 12 health's officer staffs is chosen from 10 doctors and 12 nurses. Calculate the number of ways the committee is made up of: a. 5 doctors and 7 nurses. b. not more than 6 doctors. c. at least 3 doctors and 4 nurses.
The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders' meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members) How many different slates consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval?
Six teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if: a) there must be 3 students on the committee b) there must be no more than 2 teachers on the committee c) there must be at least one teacher and at least one student on the committee d) Barry and Miss Morrison cannot be on the committee together.
How many committees could be formed from 10 students if. a) there must be at least 8 people? b) there are 5 people on the committee but Joey and Sally must be selected?
A class contaions 10 girls and 10 boys. how many 3 person committee can be formed that will give the boys a majority?
If there are 10 students, consisting of 6 men and 4 women. 1. How many ways can a committee of 4 be made? a. 215 b. 210 c. 220 d. 225 2. How many ways can a committee of 4 consisting 2 men and 2 women be made? a. 90 b. 80 c. 85 d. 95 3. How many ways can a president, vice president, secretary and treasurer be chosen? a. 1160 b. 6320 c. 5040 d. 3560
A public health unit's "Board of Health" consists of 8 citizen representatives and 9 elected officials. We want to set up a special committee from the board members, consisting of 3 citizens and 4 elected officials. How many different ways can the board members by chosen for this committee?
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7. A regional committee has 5 members from Town A, 3 members from Town B, and 2 members from Town C. If we wanted to choose a committee of 4 members, how many would have at least 2 members from Town A?