Questions: Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 5 different colors. Step 1 of 2 : How many selections of collars for the 3 cats are possible if repetitions of colors are allowed?

Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 5 different colors.
Step 1 of 2 : How many selections of collars for the 3 cats are possible if repetitions of colors are allowed?

Transcript text: Reginald wants to buy a new collar for each of his 3 cats. The collars come in a choice of 5 different colors. Step 1 of 2 : How many selections of collars for the 3 cats are possible if repetitions of colors are allowed?

Solution

Solution Steps

Step 1: Determine the Number of Choices for Each Cat

Reginald has 5 different colors to choose from for each cat's collar. Since the choice of color for one cat does not affect the others, each cat has 5 independent choices.

Step 2: Calculate the Total Number of Selections

To find the total number of possible selections of collars for the 3 cats, we use the formula for combinations with repetition, which is given by raising the number of choices to the power of the number of items (cats, in this case). Therefore, the total number of selections is:

\[ 5^3 \]

Step 3: Compute the Result

Calculate \(5^3\):

\[ 5^3 = 5 \times 5 \times 5 = 125 \]