To solve this problem, we need to use the concept of permutations.

Step 1: Understand the problem
The problem is asking for the number of ways the judge can pick out and rank the top 2 dogs out of 5. This is a permutation problem because the order in which the dogs are picked matters (i.e., Dog A being first and Dog B being second is different from Dog B being first and Dog A being second).

Step 2: Apply the formula for permutations
The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.

Step 3: Plug in the numbers
In this case, n = 5 (the total number of dogs) and r = 2 (the number of dogs to choose). So the calculation would be:

5P2 = 5! / (5-2)!
= 5*4*3*2*1 / 3*2*1
= 20

So, there are 20 different ways the judge can pick out and rank the top 2 dogs.

Question

To solve this problem, we need to use the concept of permutations.

Step 1: Understand the problem
The problem is asking for the number of ways the judge can pick out and rank the top 2 dogs out of 5. This is a permutation problem because the order in which the dogs are picked matters (i.e., Dog A being first and Dog B being second is different from Dog B being first and Dog A being second).

Step 2: Apply the formula for permutations
The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.

Step 3: Plug in the numbers
In this case, n = 5 (the total number of dogs) and r = 2 (the number of dogs to choose). So the calculation would be:

5P2 = 5! / (5-2)!
   = 5*4*3*2*1 / 3*2*1
   = 20

So, there are 20 different ways the judge can pick out and rank the top 2 dogs.

Knowee AI · Accepted Answer

To solve this problem, we need to use the concept of permutations.

Step 1: Understand the problem
The problem is asking for the number of ways the judge can pick out and rank the top 2 dogs out of 5. This is a permutation problem because the order in which the dogs are picked matters (i.e., Dog A being first and Dog B being second is different from Dog B being first and Dog A being second).

Step 2: Apply the formula for permutations
The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.

Step 3: Plug in the numbers
In this case, n = 5 (the total number of dogs) and r = 2 (the number of dogs to choose). So the calculation would be:

5P2 = 5! / (5-2)!
   = 5*4*3*2*1 / 3*2*1
   = 20

So, there are 20 different ways the judge can pick out and rank the top 2 dogs.

At a dog show there are 5 dogs competing for Best of Show. In how many orders can the judge pick out and rank the top 2 dogs?

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