Abstract Algebra: Please help with the Question below; Also include: a) Descript
ID: 3027216 • Letter: A
Question
Abstract Algebra:
Please help with the Question below;
Also include:
a) Description of method: In 1paragraphs, describe the method you used. Explain why you chose that method.
b) Approach to problem: In 1 paragraphs, discuss the motivation behind the solution, including what research you conducted and how you approached the problem.
Question:
Determine the number of ways the edges of a square can be colored with six colors in which no restriction is placed on the number of times a color can be used. Show all of your work and adequately explain your reasoning for your solution.
Answer to Question:
https://www.chegg.com/homework-help/Contemporary-Abstract-Algebra-8th-edition-chapter-29-problem-10E-solution-9781133599708
Explanation / Answer
As we know a square has four edges, and we have six colors and also it is given that there is no restriction is placed on the number of times a color can be used. So now, it is a question based on counting. As we know there are four edges and each edge can be colored with any color because there is no restriction. So we can say that,
Number of ways=6x6x6x6
which is equal to 1296.
This is because every edge can be colored with 1 out of 6 colors and each edge has 6 possibilities to color and four edges will have 1296 possibilities.