I am trying to calculate the probability of getting a full house but instead of drawing only $5$ cards, I am drawing $x$ number of cards from the $52$ card deck. I know for a $5$ card hand, I would take
$$\frac{(13\times 4) \times (12\times 6)}{52 \choose 5} = 0.00144$$
How would I generalize this to $x$ cards?