Question

Paul wants to buy a new collar for each of his 3dogs. The collars come in a choice of a 8different colors. how many selections of collars are possible if repetition of colors are not allowed?

Answer 1

The number of selections of collars that are possible if repetition of colors are not allowed is;

`336\text{ selections}`

Step-by-step explanation:

Given that Paul wants to buy a new collar for each of his 3 dogs.

And The collars come in a choice of 8 different colors.

The number of ways of selections of collars without repetition can be written as;

`P=(n!)/((n-r)!)`
`\begin{gathered} C=(8!)/((8-3)!)=(8!)/(5!) \\ C=8*7*6 \\ C=336 \end{gathered}`

Therefore, the number of selections of collars that are possible if repetition of colors are not allowed is;

`336\text{ selections}`