A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if: There are no restrictions; i) ii) B and C will serve together or not at all; D and E will not serve together. iii) State and prove Bayes' theorem

A president and a treasurer are to be chosen from a student club consisting of 50 people. How many different choices of officers are possible if: There are no restrictions; i) ii) B and C will serve together or not at all; D and E will not serve together. iii) State and prove Bayes' theorem

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...

See similar textbooks

Related questions

Q: A box contains 50 pralines made with three different types of chocolate: Dark chocolate, milk…

A: In mathematics, the method of proof by contradiction is frequently employed. It is a form of…

Q: 4. A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are…

A: Total member=9

Q: a) There are 42 students who are to share 12 computers. Each computer is shared by at most six…

Q: Q2) A club has 20 member a) In how many different ways could the club choose a president and a vice…

A: Combination only includes number of ways of selection whereas, permutation includes number of ways…

Q: Eight members of the committee will be chosen from 15 senior and 10 junior students. 13.) If there…

A: We have given that Senior students = 15 Junior students = 10 Total number of students = 15 We have…

Q: a) There are no conditions. b) There must be exactly 3 women. There must be exactly 4 men.

A: HERE AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS , PLZ REPOST FOR REMIANING PARTS WITH NOTE I…

Q: There are 5 third year and 4 fourth year students qualified to join a contest. In the group…

A: Given that there are 5 third year and 4 fourth year students qualified to join a contest. In the…

Q: I just need help with these three questions. I don't know how I got it wrong.

Q: Customers at Home Furnishings can choose from 8 kinds of coffee tables. Each coffee table comes in 3…

A: questions are based on the combination and permutation. no. of ways choosing r out of n without…

Q: A) Find the minimum number c least I of the 50 United States i

A: Introduction: If n+1 or more pigeons occupy n pigeonholes, at least one pigeonhole is occupied by…

Q: A student in a biology lab has 9 plants to use in an experiment. One plant will act as the control,…

A: Here we use the combinations for the answer, Combination: A combination is a technique that…

Q: A vice president and a secretary are to be chosen from an organization consisting of 30 people. How…

A: Note: Hi! Thank you for the question. As you have posted multiple sub-parts, according to our…

Q: None

A: Step 1: Given that, A bag contains 5 different colored marbles 8 of each color.So the total number…

Q: ) without restrictions? b) if Aamir, must be on the left end and Zeba must be on the right end? c)…

A: Here as PER POLICY I HAVE CALCULATED FIRST 3 SUBPART

Q: 3. Sophia has a bowl of 15 red, 15 blue, and 15 orange pieces of candy. Without looking, Sophia…

A: (a) Sophia has to grab (3+3+3)+1 = 10 candies to make sure she has at least 4 of the same colour.…

Q: =) A laboratory cage contains eight white mice and six brown mice. Find the number of ways of…

A: To find the number of ways of choosing five mice from the cage if i) They can be of either colour…

Q: You are a member of the BCC Math Club. The club has 15 members. a) How many different ways are there…

A: a)given, club has 15 members here n=15(total numbers) we need to select the…

Q: 7.) Consider the smallest individual cubes and assume all stacks are solid. Determine the number of…

A: Consider the first figure, the length is 6 cubes, width is 2 cubes and height is 2 cubes. Total…

Q: One survey shows that 30% of college students only work during weekdays to support themselves, 30%…

A: The objective of the question is to find out the percentage of college students who do not work…

Q: The Alhambra will be housing 4 guests from the US, 3 from IN, 2 from LK, and 1 from FR. a) In how…

A: 4 guests from US, 3 from IN, 2 from LK 1 from FR we have find a..how many different ways can the…

Q: 1) Find the number of permutations of all the letters of the w following conditions

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: C) There are 20 small towns in a district. A group of 3 people have to be chosen from I of these…

Q: There are 10 guests (1 is the host) in a conference. In how many ways can he accommodate his guests…

A: total number of guest =10 number of ways person can arrange in circular table is (n-1)!

Q: rom a group of 7 men and 5 women, how many committees of size 3 are possible. a) With no…

A: Given: No. of men=7 No. of women=5 Committee members=3

Q: The price of a turkey is the equivalent of 2 chickens or 3 ducks. With a certain amount of money I…

A: Given:The price of a turkey is equal to 2 chickens or 3 ducksYou're buying 5 turkeysFirst, let's…

Q: Suppose we want to choose 5 objects, without replacement, from 18 distinct objects. a) If the order…

A: Given,Total no.of distinct objects=18

Q: 5) The Louise Arbour basketball team of 13 players line up to take the team photograph. a) How many…

A: This question has two parts. This is related to permutation. The solution is given below.

Q: A total of 2 freshman, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a…

Q: 3) 50 employees of an organization in downtown Minneapolis were asked how they work. 21 employees…

A: The solution is given below

Q: 3. Suppose there are 6 black pens, 7 blue pens, and 5 red pens. Find the number of ways you can…

A: Given,no.of black pens=6no.of blue pens=7no.of red pens=5Total no.of pens=18

Q: the following problems using Venn Diagram and answer the question? irty-five ladies were interviewed…

A: Please refer to the image below

Q: An investment counsellor would like to meet with 10 of his clients on Tuesday, but he has time for…

A: Given: n=10 r= 8

Q: From a group of 10 men and 5 women, how many committees of size 5 are possible? a.) With no…

A: Given From a group of 10 men and 5 women, how many committees of size 5 are

Q: Show all work!

A: Step 1: Problem 6: To find the probability of winning either the first or second prize, we need to…

Q: If A = {3,4,7,9) and K = {1,3,4}, find A UK.

A: As per policy, we are solving only the first question please post multiple questions separately.

Q: .) there are no restrictions b.) one particular person must be chosen on the committee? c.) one…

A: A committee of 5 people is to be chosen from a group of 6 men and 4 women total persons are 10 here…

Q: A survey of farmers showed that of the farmers, 124 grew only wheat, 108 grew only corn, 89 grew…

A: Here we will use venn diagram to find values of each type .

Q: QS- Five friends meet at the local cafe, where each of them orders one soft drink. In how many ways…

A: Follow the steps

Q: d) There can be no men. e) There must be at least 3 men.

A: Here given , There are total 10 people available for making committee of 5 member. There are 6…

Question

A president and a treasurer are to be chosen from a student club consisting of 50
people. How many different choices of officers are possible if:
There are no restrictions;
i)
ii)
B and C will serve together or not at all;
D and E will not serve together.
iii)
State and prove Bayes' theorem

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

c) There are three train tracks from village X to village Y and four train tracks from village Y to village Z. i) How many ways to travel from village X to village Z via village Y by train? ii) How many different round-trip routes are there from village X to Y to Z to Y and back to X in which the same road cannot be travelled twice?
Q2) A club has 20 member a) In how many different ways could the club choose a president and a vice president? b) In how many different ways could the club choose two co-presidents? c) In how many different ways could the club choose a president, vice- president, and secretary? d) In how many different ways could the club choose a three-member governing committee? e) In how many different ways could the club choose two co-presidents and a secretary?
a class consists of 37 freshmen, 54 sophomores, and 22 juniors. The class wantsto send a nine-person delegation to the university sentate a) if the delegation has to consist of 2 freshman 3 sophomore, and 4 juniors, how many different delegation are possible? b) If the nine-person delegation is chosen without regard to class standing, how many delegations are possible?
Computer programming team has 13 members. B.) Suppose 7 are women and 6 are men. How many groups of 5 can be chosen to only one being a man? B2) Suppose 2 insist on working together or not at all on projects. How many groups of 5 can be chosen to work on a project?
2) A class has 25 students. Each day, three students are chosen to present their work at the board. In total, how many such 3 student groups are possible?
Major League Baseball teams maintain a 25- man roster and also a 40- man roster. Players on the 25- man roster may play in official games throughout the season. The additional 15 players on the 40- man roster may play in games starting September 1. a) how many 9-player batting orders are possible from a 25-man roster? b) How many 9-player batting orders are possible from a 40-man roster?
Consider the jumbling letters of the word " ARIES " under the following given conditions , 1. List all the words , where all the vowels are together and count all the total possibilities . ii . List all the words where the vowels and consonants are in alternate places , and count all of them . lii . If not all vowels at same place without exactly listing , calculate how many such words are possible .
Please answer letter c to letter e
a).A food-processing firm has 8 brands of seasoning agents from which it wishes to prepare a gift package containing 5 seasoning agents. How many combinations of seasoning agents are available? b). A sales person has 9 products to display in a trade fair but he can display only 4 at a time, how many displays can he make if the order in which he displays is important? c).A radio repairer notes that the time he spends on his job has an exponential distribution with a mean of 4 minutes. He follows the first come first serve principle. The arrival time of clients takes a Poisson distribution with an average rate of 8 clients every 1 hour. i.Determine the arrival rate value and service rate value to be used ii) How long will it take the client waiting in the queue iii). Determine the client’s average waiting time in the system iv).Compute the probability that the system is idle; P (idle)
e) d) In how many ways can the letters of the word "OPTOM" be arranged? Show work. A committee of 3 is to be formed from a group of 20 people. How many different committees are possible? Show work. f) From a group of 5 women and 7 men, how many different committees consisting of 2 women and 3 men can be formed? Show work.