A builder is planning to build 12 houses along one side of a road. He willbuild 2 houses in style A, 2 houses in style B, 3 houses in style C, 4 houses instyle D and 1 house in style E.(i) Find the number of possible arrangements of these 12 houses.(ii)RoadFirst groupSccond groupThe 12 houses will be in two groups of 6 (see diagram). Find the numberof possible arrangements if all the houses in styles A and D are in the firstgroup and all the houses in styles B, Cand E are in the second group.(iii) Four of the 12 houses will be selected for a survey. Exactly one housemust be in style Band exactly one house in style C. Find the number ofways in which these four houses can be selected.

Given data: The total numbers of houses are n=12. The number of styles A house is A=2. The number of…

Answered: A builder is planning to build 12…

A builder is planning to build 12 houses along one side of a road. He will build 2 houses in style A, 2 houses in style B, 3 houses in style C, 4 houses in style Dand 1 house in style E.

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: Maria has 10 different photos, and she wishes to arrange 5 of them in a row. In how many ways can…

A: Giventhere are 10 different photos

Q: The Goal Line Gals has 35 members and the Baseball Babes has 28 members. At a joint meeting all…

A: Let's denote the set of members in the Goal Line Gals as G and the set of members in the Baseball…

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 24 pieces. How many different…

Q: There are 40 pieces of candy in Josh's bag. If - of the 8 candy are bags of M & M's, how many bags…

A: Given there are 40 pieces of candy in Josh's bag. 18 of the candy are bags of M & M's. We have…

Q: A pianist plans to play 6 pieces at a recital from her repertoire of 24 pieces. How many different…

A: Given data A pianist plans to play 6 pieces at a recital from her repertoire of 24 pieces

Q: The slope field above is drawn in the ty-plane. Add these two solutions to the slope field: • Sketch…

A: We are given the following slope field in the ty - plane. The sketch of the approximate solution…

Q: Your little cousin will have a big animal-themed birthday party and you will help with goody bags.…

Q: Reading interventions - Jasmine is a reading curriculum specialist for a large urban school…

Q: Given that a =(-5, 1), b = (-5, -2), and c = (-1, 1), find the number. (Round your answer to one…

A: Find your answer below

Q: the store received 54 new books to place on 6 displays. The same number of books will be placed on…

A: To find out how many books will be placed on each display, you can divide the total number of new…

Q: A department store manager wants to display 6 brands of a product along one shelf of an aisle. In…

A: According to the provided information, A department store manager wants to display 6 brands of a…

Q: A pianist plans to play 3 pieces at a recital from her repertoire of 25 pieces. How many different…

A: As per given by the question, a pianist plans to play 3 pieces at a recital from her repertoire of…

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 22 pieces. How many different…

A: Permutation formula: nPr = n!/(n-r)!

Q: This is the idea of a slope field graph: 1. Our goal is to sketch the unknown function y (t). 2. We…

A: Basic propoerties of the curve y(t). The curve y(t) touches the tangent at every point. It never…

Q: A man is 6 feet tall and his shadow measures 5 feet. If the shadow of a tree near the man measures…

Q: You and 3 friends are moving into a new apartment-style dorm. The dorm has 3 bedrooms, one with two…

A: There are totally 4 members. These 4 members must be arranged in 3 bed rooms. One bedroom has two…

Q: I only need answer to number 20 and 27.

A: We have to find the slope of the line and graph the given equation.First we will compare it to the…

Q: A preschool teacher is rearranging four boxes of playing blocks so that each box contains an equal…

A: Given: Box 1 = 32 blocks Box 2 = 18 blocks Box 3 = 41 blocks Box 4 = 9 blocks

Q: Yield from an Apple Orchard Figure (shown below) is a graph of the annual yield, y(t), in bushels…

Q: O Sarah plans to contribute monthly to a savings account for her daughter's coll goal is $300,000 in…

A: The future value is calculated using the formula Future value FV=C1+in-1i where i is the interest…

Q: 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40 60 80 (d) Use a graphing utility to approximate…

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: If bailey has 7 bananas and she got 2 more how Many does she have in total?

A: Given, Initially bailey has 7 bananas Then She got 2 more bananas We have to find the Total number…

Q: Juan made 13 out of 20 free throws. If Bonita shoots 25 free throws, what is the minimum number he…

A: Note: Hi there! Thank you for posting the question. To avoid the plagiarism issue we have used the…

Q: ianist plans to play 6 pieces at a recital from her repertoire of 26 pieces. How many different…

A: Total number of pieces available (n) = 26 pieces. Number of pieces (r) which a pianist needs to play…

Q: (Sec. 2.4) A department store sells sport shirts in three sizes (small, medium, large), three…

Q: Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let u…

Q: Recall that equations representing sequences can be written in the form t (n) = mn + b or t (n) =…

A: topic - arithmetic sequence

Q: Ms. Karen has 7 children in her preschool class. She would like to give each student an equal number…

A: Solution is given below:

Q: A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces. How many different…

A: Given : No. of repertoire pieces = 25 A pianist plans to play 4 pieces i.e n = 4

Q: If Snow White polishes the diamonds that the seven dwarves mine and bring home, she gets to keep 1/8…

Q: 5. * y -2 4 0 2 10

A: (5) From the given table consider the two pair equation of the line passing through…

Q: I gathered together a bunch of my friends and a bunch of money. Read carefully on how I gave my…

A: According to the question, a certain amount of money is equally distributed among some friends.…

Q: If Sammy has 24 candy bars and Jaycob has 4 more than Sammy how many candy bars does jaycob have

Q: A contractor needs to plant 5 Oak trees, 9 Maple trees and 6 Poplar trees in a straight line. How…

Q: what would side AB be to the nearest hundred?

A: Given traingle is right angle triangle

Q: bakery receives an order for 1,600 cookies. if 12 cookies are packed in each bag, will 132 bags bags…

A: Given that a bakery receives an order for 1,600 cookies. if 12 cookies are packed in each bag, will…

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

A builder is planning to build 12 houses along one side of a road. He will
build 2 houses in style A, 2 houses in style B, 3 houses in style C, 4 houses in
style D and 1 house in style E.
(i) Find the number of possible arrangements of these 12 houses.
(ii)
Road
First group
Sccond group
The 12 houses will be in two groups of 6 (see diagram). Find the number
of possible arrangements if all the houses in styles A and D are in the first
group and all the houses in styles B, Cand E are in the second group.
(iii) Four of the 12 houses will be selected for a survey. Exactly one house
must be in style Band exactly one house in style C. Find the number of
ways in which these four houses can be selected.

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

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

i need number 8, a and b
if Jake got 5 apples and Katie takes away 3 how many apples will he have?
What would be the answer to number 2,3,5,6 and, 7?
I would like answer to number 2,3,4 please
Mr Mathews owns a few ice-cream trucks. If he places 5 workers in each truck, he will have 3 extra workers. If he places 7 workers in each truck, he will need 25 more workers. How many ice-cream trucks does Mr Mathew own?
I don't get how to get the sides for number 9.
i need Solution of 11, 12, 13 parts
Please answer the question(s) with the same format as the examples. Thank you.
I only need answers to letter d, e, f. Please answer those 3 letters only NOT a, b, c.
A pianist plans to play 6 pieces at a recital from her repertoire of 26 pieces. How many different recital programs are possible?
Meredith works at a blood bank. She needs to write a report of the ratio of type- a blood donated to tpye-o blood donated, but she lost this month's logs that had the quantities. She knows that last month 25 pints of tpye-a blood were donated and 42 pints of tpye-o blood were donated. She remebers that this month 55 pints of tpye-a blood were donated. if the ratio held true for this month, how can Meredith determine the amount of tpye-o blood donated