I am solving an equation to find the probability that the first card of a standard, 52 card deck is a king or a heart, and I feel like I’m doing this wrong.

I set up this equation (k for king, h for heart):

$P(k$ or $h)=P(k)+P(h)$ $-(P(k) \cdot P(h))$

I first solved for $P(k)$. I knew that the denominator of $P(k)$ would be the permutation of every card in the deck:

${ }_{52} P_{52}=52 !$

I solved for the numerator by figuring out the permutations of all the cards after the king, then I multiplied by four because there are 4 kings.

${ }_{51} P_{51} \cdot 4=51 ! \cdot 4$

I then knew $P(k)=\frac{51 ! \cdot 4}{52 !}$

I already knew the denominator for $P(h)$ was $52 !$, so all I needed to do was find the numerator. It was going to be $51!$ times the amount of hearts that there were, so $13$

I then knew:

$P(h)=\frac{51 ! \cdot 13}{52 !}$

Now that I know $P(h)$ and $P(k)$, I could solve the equation:

$P(k$ or $h)=\frac{51 ! \cdot 4}{52 !}+\frac{51 ! \cdot 13}{52 !}$ $-\left(\frac{51 ! \cdot 4}{52 !} \cdot \frac{51 ! \cdot 13}{52 !}\right)$

I know that $\frac{51 !}{52 !}=\frac{1}{52}$, so I simplified down to:

$P(k$ or $h)=\frac{4}{52}+\frac{13}{52}$ $-\left(\frac{4 \cdot 13}{52^{2}}\right)$

$ =\frac{17}{52}-\frac{52}{52 \cdot 52} $

$ =\frac{17}{52}-\frac{1}{52} $

$ =\frac{16}{52} $

Did I solve this correctly? I was also wondering if there was a better way to do this.

Thank you!