In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?
Choose the most appropriate option.
A) 6 B) 8 C) 9 D) 10 E) 12
The question has a catch.. It would seem on the face of it it would be 3 x 3 x3 = 27 arrangements, but what it is asking is how many arrangements the family leaves with.. so that is going to be   Pick all 3 = 1 way   Pick all of a kind = 3 x 1 = 3 ways   Pick 2 of a kind = 3 x 1 x 2 = 6 ways   Total of 10   ANS:10
<result>D</result>
In a family with 3 children, the parents have agreed to bring the children to the pet store and allow each child to choose a pet. This pet store sells only dogs, cats, and monkeys. If each child chooses exactly one animal, and if more than one child can choose the same kind of animal, how many different arrangements of animals could the family leave with?