Maths

[Guest]

the village of petiville allows each household to own maximum of 2 dogs, 4 cats and 5 birds. if Adams family has atleast 2 of each of these 3 types of pets , how many different combination of numbers of each type of pet would there be?

[HallsofIvy]

Since they say "at least 2 of each of these 3 types of pets" I would start with the basic (2, 2, 2). We are also told that there can be a maximum of "2 dogs, 4 cats and 5 birds" so we cannot change the number of dogs but we can have
(2, 2, 2)
(2, 2, 3)
(2, 2, 4)
(2, 2, 5)
(2, 3, 2)
(2, 3, 3)
(2, 3, 4)
(2, 3, 5)
(2, 4, 2)
(2, 4, 3)
(2, 4, 4)
(2, 4, 5)

If you don't like actually listing the possibilities you can calculate that there is only one possible choice of number of dogs, 2, 3 possible choices for the number of cats, 2, 3, and 4, and 4 possible choices for the number of birds, 2, 3, 4, and 5, so a total of 1(3)(4)= 12 possible choices.