To solve this problem it is necessary to use the multiplication counting rule, that states that if there are two events a and b, the total number of outcomes will be a times b (a*b).
In this case, the total number of outcomes will be the product of the number of options for each event (cages, kinds of wood shavings and water bottles).
[tex]2\cdot5\cdot2=20[/tex]Baldwin's family can set up a home for their hamster in 20 different ways.