To do this you have to add a lot of combinations

To have at least mean you can have more so you have to add up all the combinations where you have exact amounts.

Start with only aces and kings

There are 4 aces and 4 kings to select from.

There are

4C3 + 4C1 to draw 3 aces and 1 king.

4C2 + 4C2 to draw 2 aces and 2 kings

4C1 + 4C3 to draw 1 aces and 3 kings

Then do this with the other 46 cards

4C2 + 4C1 + 46C1 to draw 2 aces and 1 king and 1 of something else.

4C1 + 4C2 + 46C1 to draw 1 ace and 2 kings and 1 of something else.

4C1 + 4C1 + 46C2 to draw 1 ace and 1 king and 2 of something else.

Add all these up to get the total number of ways you can draw 4 cards with at least 1 ace and 1 king.

On the site calc use this nCr(4, 3) for 4C3

One of moderators should check that I not make a mistake. Maybe there is a easier way to do this too.