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?

Question

Stephany Hart

Mathematics

12 March, 20:01

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?

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Naomi Wiggins · Answer 1

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.