Reginald wants to buy a new collar for each of his 3
dogs. The collars come in a choice of 7
different colors.
Step 2 of 2 : How many selections of collars are possible if repetitions of colors are not allowed?
To find the number of selections of collars possible if repetitions of colors are not allowed, we can use the concept of permutations.
The number of ways to choose a collar for the first dog is 7 (since there are 7 different colors available).
The number of ways to choose a collar for the second dog is 6 (since we cannot repeat the color chosen for the first dog).
The number of ways to choose a collar for the third dog is 5 (since we cannot repeat the colors chosen for the first and second dogs).
Therefore, the total number of selections possible is:
7 x 6 x 5 = 210
So, there are 210 possible selections of collars when repetitions of colors are not allowed.