As it stands, I cannot justify either of those answers.
The problem is clearly how one goes about disturbing the legs.
There are 36 basic forms using the three different heads, bodies, and tails.
But the legs are problematic. Do you count the dog legs as one set that must go together? If so there are just two to distribute those because the bird body has only two legs and must get the bird legs. In that case we have 72 possible mutants. That is close to your fatherís answer.
However, if we have ten individual legs then matters a vastly more complicated? That is still true if we consider the four dog legs identical as well as the cat and bird legs. In this case we could have an animal with a bird head, cat body, dog tail and two dog legs, a cat leg & a bird leg.
So please try to clarify this statement.