Let's deal with the restrictions first.
To get one ace, we have 4 total aces, and we want to choose one ace:
[tex]\text{One ace: } ^{4}C_1[/tex]
We can repeat this for the king, as well.
[tex]\text{One king: } ^{4}C_1[/tex]
Now, let's deal with the remaining five cards.
Since we can't deal a king or an ace anymore, let's subtract 8 from a pack of 52. This ensures that we don't pick a king or an ace anymore.
Now, we simply need to pick five cards from a pack of 44 cards:
[tex]\text{Five cards: } ^{44}C_5[/tex]
Thus, the total number of ways to pick exactly one ace and one king is:
[tex]^{4}C_1 \cdot ^{4}C_1 \cdot ^{44}C_5[/tex]
The calculator should do the rest.
