Question

Ben wants to buy a new collar for each of his 5 dogs. The collars come in a choice of 9 different colors. Step 1 of 2 : How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed

Answer 1

The total number of selections of collars Ben can make for his 5 dogs, with 9 different colors and repetitions allowed, is 59,049. This is calculated using the principle of multiplication, raising the number of color options to the power of the number of dogs, which is 9 to the power of 5.

Step-by-step explanation:

Ben wants to buy a new collar for each of his 5 dogs and there are 9 different colors to choose from, with repetitions of colors allowed. To calculate the total number of selections possible, we use the principle of multiplication for counting. This principle states that if you have n choices for one decision, and m choices for a second decision, you have a total of n × m choices for the two decisions combined.

In Ben's case, for each dog, there are 9 choices of color. Since there are 5 dogs and the choices are independent (the choice for one dog's collar color doesn't affect the others), we multiply the number of choices for each dog. So the mathematical expression is 9 × 9 × 9 × 9 × 9, or 95, which represents the total number of possible combinations.

Calculating 95 gives us a total of 59,049 different selections of collars that Ben can make for his 5 dogs.

Answer 2

59049 ways

Step-by-step explanation:

Given

`Colors = 9`

`Dogs = 5`

Required

Determine number of selection (repetition is allowed)

The number of collars is not given.

So, we'll assume that there are enough collars to go round.

If no repetition is allowed, each of the 5 dogs have 9 colours to select from.

i.e.

`Dog\ 1 = 9`

`Dog\ 2 = 9`

`Dog\ 3 = 9`

`Dog\ 4 = 9`

`Dog\ 5 = 9`

So, the number of selection is:

`Selection = 9 * 9 * 9 * 9 * 9`

`Selection = 59049`