a) If I draw 5 cards randomly what are the chances of getting a full house ?
b) Which other card can you remove to maximize your chances of getting full house?
So you have in total 56 cards, the 4 added cards are a new king for each type. I do not really know how to do this.
We have $56$ cards with $8$ kings and rest $48$ cards are of $12$ ranks similar to a standard $52$ cards pack.
a) Possibility $1$ for getting a full house -
We have two ranks without king -
So we first select which two ranks from: $1$ to $10$ and $J, Q, A$ and then any of the chosen two can be $3$ cards and the other $2$. That is,
$2 \cdot {12 \choose 2} {4 \choose 3} {4 \choose 2}$ possibilities
b) Possibility $2$ for getting a full house -
One of the ranks is king and so we choose $1$ rank from remaining $12$ ranks. Then we either have $3$ cards of king and $2$ of the other or $2$ cards of king and $3$ of the other. That is,
${12 \choose 1} \big[{8 \choose 3} {4 \choose 2} + {8 \choose 2} {4 \choose 3})\big]$ possibilities.
Total count of favorable possibilities is sum of $(a)$ and $(b)$ and then to find desired probability, we divide by
c) Total possibilities without restrictions, which is ${56 \choose 5}$.