Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Using the arrangements formula, the number of orders is given as follows:
- 39,916,800 if no restrictions.
- 86,400 if they are lined up alternatively.
- 7,257,600 if the first and last must be cats.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are no restrictions, the number of ways is:
[tex]A_{11} = 11! = 39,916,800[/tex]
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]
When the first and last are cats, we have that:
- For the first and last animals, there are 5!/2! = 20 ways.
- For the middle 9 animals, there are 9! ways.
Hence:
20 x 9! = 7,257,600.
More can be learned about the arrangements formula at https://brainly.com/question/24648661
#SPJ1
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.