We appreciate your visit to You have 3 identical red flags 4 blue flags and 7 yellow flags Determine how many ways you can arrange all the flags on a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final Answer:
The red flags are treated as a single unit, resulting in 12 units. Using the formula [tex]\(\frac{12!}{3! \times 4! \times 7!}\)[/tex]e the flags with a red flag first. This accounts for identical arrangements within each color. Thus the correct option is c) 132 ways
Explanation:
To determine the number of ways to arrange the flags on the pole with a red flag first, we can treat the three red flags as a single unit. Now, we have 1 red unit, 4 blue flags, and 7 yellow flags, making a total of 12 units. These units can be arranged in 12! (12 factorial) ways.
However, since the flags within each color are identical, we need to correct for overcounting. The red flags can be arranged among themselves in 3! ways, the blue flags in 4! ways, and the yellow flags in 7! ways. Therefore, the total number of arrangements is given by:
[tex]\[ \dfrac{12!}{3! \times 4! \times 7!} \][/tex]
Simplifying this expression, we get:
[tex]\[ \dfrac{479,001,600}{6 \times 24 \times 5,040} \][/tex]
Which equals 132. Therefore, there are 132 ways to arrange the flags on the pole with a red flag first.
In summary, the final answer is 132 ways because we consider the red flags as a single unit and correct for the arrangements within each color. The formula used ensures that we account for the identical nature of the flags within each color, providing an accurate count of the unique arrangements. Therefore, the correct option is c) 132 ways
Thanks for taking the time to read You have 3 identical red flags 4 blue flags and 7 yellow flags Determine how many ways you can arrange all the flags on a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
