Arranging professors, cats, and dogs

Question

A math professor invites all of his students over for a party. Assume $n$ students show up, and each student brings a cat and a dog.
A) Assume the cats, dogs and students are distinguishable from each other. If all of the cats, dogs, students line up how many different ordering are there?
B)Assume the cats, dogs are indistinguishable because they are the same breed, but the students are distinguishable. If all the cats, dogs and students line up how many different ordering are there.

Answer 1

When all animals and students are distinguishable from each other, then the number of line-ups is the number of permutations of all $3n$ of inviduals.

When cats are indistinguishable from each other, and dogs are indistiguishable form each other, then first pick $n$ places where cats will be standing, then pick $n$ places where the dogs will be standing, then line up the studentsin the remaining spaces.

If you still have problems, show what you have tried.

Answer 2

For case B) it will be $\frac{(3n)!}{n!n!}$ (permutations with repetitions as you have two sets of $n$ repeating elements)