Q: What is the probability that you have $x$ spades and your partner has $y$ spades. I have to show that the probability is
$$\frac{ {13 \choose x  } { 39 \choose 13 - x} {13 -x \choose y  } { 26+x \choose 13-y} }{{52 \choose 13  } { 39 \choose 13} }.$$
I can see that $ {52 \choose 13  } { 39 \choose 13} $ is the number of ways you can deal hands.
$ {13 \choose x  } { 39 \choose 13 - x}$ is the number of ways of selecting $x$ spades and selecting the remaining cards in the hand to be not spades.
${13 -x \choose y  }$ is the number of spades $y$ to get from the remaining $13-x$ spades.
I am not seeing where  ${ 26+x \choose 13-y}$ is coming from.

A: Originally there are $39$ non-spades.  The first player will use $13-x$ of those.  After the first player has their non-spades selected, there still remain $39-(13-x)$ non-spades for the second player to choose from.
Recognize: $39-(13-x) = 39-13-(-x)=26+x$.  That is where it is coming from, it is coming from how many ways there are to pick which non-spades that the second player is getting.  We have $26+x$ options for non-spades left to choose from, and we need to pick $13-y$ of those for the second player to receive.
