[AaronBrown]

Here is another way to think about it.

Regardless of the sexes of the first three puppies, there's a 50/50 chance that the fourth puppy will make it 3-1. If the first three are 3-0, the fourth can the the opposite of the 3. If the first three are 2-1, the fourth can be the same as the 2.

But to get 2-2, the first three have to be 2-1, then there's a 50/50 chance the fourth puppy is the same as the 1. If the first three are 3-0, you can never get 2-2.

So half the time you get 3-1, and half of three-quarters of the time, you get 2-2.