Reginald wants to buy a new collar for each of his 3
dogs. The collars come in a choice of 7
different colors.
Step 1 of 2 : How many selections of collars for the 3
dogs are possible if repetitions of colors are allowed?
Since repetitions of colors are allowed, for each dog, there are 7 choices of colors. Therefore, the total number of selections of collars for the 3 dogs is:
7 choices for dog 1 * 7 choices for dog 2 * 7 choices for dog 3 = 7^3 = 343
Therefore, there are 343 possible selections of collars for the 3 dogs if repetitions of colors are allowed.