We have 5 books, including books A and B. We place them randomly on an empty shelf, one next to the other. In how many ways can they be placed so that: (a) books A and B do not stand next to each other b) two other books stand between books A and B?

We have 5 books, including books A and B. We place them randomly on an empty shelf, one next to the other. In how many ways can they be placed so that: (a) books A and B do not stand next to each other b) two other books stand between books A and B?

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: 2. Eight persons are to be assigned to two different rooms. Let A one room must have 3 persons. B…

A: Probability can be found by using combinations.

Q: On Monday, Tom worked 2 hours and Sylvester worked 3 hours and they made a total of 23 mouse traps.…

Q: If n(A) = 12, n(A ∪ B) = 30, and n(A ∩ B) = 6, find n(B).

Q: Is there a difference in the car brand's countries for Midwesterners and people from the west coast?…

A: From the randomly selected Midwesterners who were surveyed, had an American car, had a car from…

Q: a. no three digits are to be the same? b. the number must be odd? c. the number must be even?

A: here given 5 digit number formed from the digits 1,2,3,....9 so there are 9 digit available for…

Q: A volleyball team has ten players. To play a game, 6 players are needed to play positions numbered…

A: No. of players in the volleyball teamNo. of players needed to playThe positions are numbered from…

Q: Question 9.7) There are 3 Grey Shirts,5 Orange Shirts and 4 Blue Shirts in a suitcase.Gary selects 4…

Q: n how many ways can 5 men, 4 women, and 3 children be arranged in a row of 12 seats if a. the men…

A: Given that Number of men = 5 Number of women = 4 Number of children = 3 Number of seats in the row…

Q: List the outcomes that comprise the event (X U Z)

A: Given: The 4 finalists are : Anne, Ben, Collin, Daisy Sample space AB, AC, AD, BC, BD, CD, BA, CA,…

Q: 200 people were asked which of these sports they have attended. The sports inquired about were: UAAP…

A: Given that 200 people were asked which of these sports they have attended. The sports inquired about…

Q: A garderning company is planting trees and flowers at 3 sites on the median of a new road. For each…

A: * SOLUTION :-

Q: There is a drawer with a total of 7 socks in it. Four (4) socks are blue and three (3) socks are…

A: Four (4) socks are blue and three (3) socks are yellow

Q: Compute the number of ways you can select n elements from N elements for each of the following: a. n…

A: a. b. c.

Q: (b) A committee of 10 people is to be chosen from a group of 12 men and 8 women. How many committees…

Q: As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color…

A: a. Out of 52 cards, there are four "7" cards (each suit has one "7" card). If a card is randomly…

Q: If P( A U B) = 0.5 , P (B) = 0.2, P (A)=0.4 then || P(B|A) Is?

A: GivenP(A∪B)=0.5P(B)=0.2P(A)=0.4

Q: In how many ways can you arrange 6 distinct maths books and 5 distinct physics books on a shelf, if…

Q: 15. A rug manufacturer has decided to use five compatible colors in her rugs. However, in weaving a…

A: Given that For Rug manufacturer Number of colors=5 In a Rug weaving Number of spindles=4 We…

Q: Benny is a messy student who keeps all his colored socks in a box. The box contains a total of 4…

A: Given: Number of blue socks = 4 Number of yellow socks = 2

Q: On Monday, tom worked 2 hours and Sylvester worked 3 hours and they made a total of 23 traps. On…

A: Let 'x' be the number of traps Tom does 'y' be the number of traps Sylvester does 'z' be the number…

Q: Shirley and Ben are going souvenir hunting. They come across a store that sells all sorts of…

A: (i) The objective is to find the number of ways to assign 75 key chains in 6 bags. That is, 75 key…

Q: After a late night of math studying, you and your friends decide to go to your favorite tax-free…

A: It is given that the total amount is $16. The number of items is 8 the entire amount has to be…

Q: Imagine a game show on television where one lucky contestant is presented with three upside-down…

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

Q: Emily is having a birthday party. a. There are 25 kids in Emily’s class (including herself). Her…

A: Part (a) Given that, "E" invited 7 friends including her best friends "J", "M" and "R". She already…

Q: Suppose that you have 7 cards. 3 are green and 4 are yellow. The 3 green cards are numbered 1, 2,…

A: Given: Number of green cards = 3 Number of Yellow cards = 4 Total number of…

Q: If Joe only has room for 2 of his 6 flags on his flagpole, how many different ways can they be…

Q: A canteen offers 4 choices of appetizers, g choices of main meals and 5 choices of desserts. A…

A: Given : A canteen offers 4 choices of appetizers, 8 choices of main meals and 5 choices of desserts.…

Q: Mr. Arboreta wants to plant fruit trees in a rectangular array. For each of the following numbers…

A: A number of objects or elements arranged in a row and Column is called a rectangular Array. In that…

Q: A woman wants to select 5 pair of shoes from six pairs of red shoes, 4 pairs of white shoes and 3…

A: Pair of shoes women want is 5. Pair of red shoes is 6. Pair of white shoes is 4. Pair of black shoes…

Q: Q.7| Ten people have a potluck. Five people will be sekected to bring the main dishes, three people…

A: Given Information: Total people = 10 People who will bring main dish = 5 People who will bring…

Q: 6. Given the following statistics, what is the probability that a woman has cancer if she has a…

Q: You are dealt 5 cards from a standard 52 card deck (order doesn't matter and without replacement).…

A: Answer:----. Date:----11/10/2021

Q: Suppose you want to get a license plate. The license plate has to have 3 letters without repetition,…

Q: . Over the past year, John has purchased 30 books.(a) In how many ways can he pick four of these…

A: Permutation is an arrangement or order of selecting some of the elements from a group or a set of…

Question

3.70 We have 5 books, including books A and B. We place them randomly on an empty shelf, one next to the other. In how many ways can they be placed so that:
(a) books A and B do not stand next to each other
b) two other books stand between books A and B?

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Last Super Bowl weekend, there were 109 pizzas ordered for the sophomore dorm. That weekend 32 customers ordered their pizza with just pepperoni, 40 ordered their pizza with just sausage, 18 ordered theirs with just onions, 13 ordered theirs with pepperoni and sausage, 10 ordered theirs with sausage and onions, 9 ordered theirs with pepperoni and onions, and 7 ordered theirs with all three items. (a) How many customers ordered their pizza with pepperoni or sausage (or both)? (b) How many customers ordered their pizza with sausage or onions (or both)? (c) How many customers ordered a pizza without pepperoni, sausage, or onions?
If n(B) = 24, n(A ∩ B) =5, and n(A ∪ B) = 42, find n(A). 24 23 25 21
#4 only ty
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Anne, Ben, Collin, and Daisy. The possible outcomes can be represented as follows. АВ, АС, AD, BC, BD, CD, ВА, СА, DA, CВ, DB, DC Here, for example, AD represents the outcome that Anne receives the first prize and Daisy receives the second prize. Let = event that Collin gets first prize Y = event that Daisy gets a prize Z= event that both price winners are boys.
Pls help ASAP
You have one pile of 11 building blocks, each one a different color, and you also have another pile of 7 blocks, again each one a different color. How many ways are there to build a tower 4 blocks high from the first pile and another tower 3 blocks high from the second pile? Assume that the colors at each level of a tower matter.
3: At a Chinese restaurant, dinner for 8 people consists of 3 items from column A, 4 items from column B and 3 items from column C. If columns A, B and C have 5, 7 and 6 items respectively how many different dinner combinations are possible?
You are going to a bakery and they are selling bread (B), doughnuts (D) and cookies (C). A. If you are only going to buy two different items, list all of the permutations. B. If you are only going to buy two different items, list all of the combinations.
A canteen offers choices of appetizers, 8 5 choices of 4 choices of main meals and desserts. A customer can choose to eat just one course or two different courses or all three different courses. Assumig all choices are available how many different possible meals does the restaurant offer? A. 160 B. 269 C. 252: D. 17. E. None of the above.
D. 120 D. 480 ciation grams ates 13. Which of the following expressions represents the number of possible ways choosing 3 different kinds of food from a menu of 10? 10! A. 10! C. (10-3)! (10-3):3! 10! set of B. D. (10-3)! 3! 10! es to attend 14. In how many ways can 8 people be seated n the class around a circular table if two of them insist on sitting beside each other? A.360 C. 1440 o the B. 720 D. 5040 15 In how many ways can 6 diamonds be arranged in a circular bracelet? C. 10 A. 4 D. 120 B. 6
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Anne, Ben, Collin, and Daisy. The possible outcomes can be represented as follows. АВ, АС, AD, BC, BD, CD, ВА, СА, DA, CВ, DB, DC Here, for example, AD represents the outcome that Anne receives the first prize and Daisy receives the second prize. Let = event that Collin gets first prize Y = event that Daisy gets a prize Z= event that both price winners are boys.
Quen: In a pharmaceutical study, two drugs (A and B) and a placebo are to be compared for effects. Fifty people are to be used in the study, of whom 20 are to receive drug A, 20 receive drug B, and the remainder receive the placebo. Assuming the people are numbered 1 to 50, how many different ways could the assignment of the drugs and placebo be made?