Answer:
The number of selections of collars that are possible if repetition of colors are not allowed is;
[tex]336\text{ selections}[/tex]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;
[tex]P=\frac{n!}{(n-r)!}[/tex][tex]\begin{gathered} C=\frac{8!}{(8-3)!}=\frac{8!}{5!} \\ C=8\times7\times6 \\ C=336 \end{gathered}[/tex]Therefore, the number of selections of collars that are possible if repetition of colors are not allowed is;
[tex]336\text{ selections}[/tex]