Question

Dave wants to buy a new collar for each of his 3 dogs. The collars come in a choice of 6 different colors. 1. How many selections of collars for the 3 dogs are possible if repetitions of colors are allowed? 2. How many selections of collars are possible if repetitions of colors are not allowed?

Answer 1

Answer:

1: 216 selections

2: 120 selections

Step-by-step explanation:

1:

we have 6 different colors and we can choose the same color repeatedly, so for each of the 3 dogs, we have 6 possibilities, so the number of combinations is 6*6*6 = 216 selections.

2:

we have 6 different colors and we can't repeat a color, so the first collar has 6 possibilities, the second has 5 possibilities (one color was already chosen), and the third collar has 4 possibilities (two already chosen), so the number of selections is 6*5*4 = 120.