We want to divide 10 dogs (including Fluffy and Nipper) into three groups, one with 3 dogs, one with 5 dogs, and one with 2 dogs. How many ways can we form the groups such that Fluffy is in the 2-dog group and Nipper is in the 5-dog group?
We have 10 dogs in the following groups
fluffy plus 1 more
Nipper plus 4 more
A group of three.
8C3 ways to choose the 3 then 5 ways to get the one the rest go in with nipper
8C3 *5 = 56*5 = 280 ways