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...

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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.

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