Question

This is a two-part questionDave wants to buy a new collar for each of his three cats. The collars come in a choice of five different colors.How many selections of collars for the three cats are possible if repetitions of colors are allowed.Part 2: How many selections of collars are possible if repetitions of colors are not allowed

Answer 1

1) Notice that there are three cats, and each collar has 5 options (colors).

2) Based on that, we can write the following, considering the repetitions of colors are allowed.

Thus, there are 125 possibilities (selections) for picking colors for this set of three collars.

Part 2) Given that now, it is not allowed repetitions we can use the same diagram with a little adjustment: the number of possibilities over the dash is going to be decreasing for each picking means one less option.

Since Dave cannot repeat any color, there are now 60 selections to be made.