How many 6 card hands are possible with a 13-card deck?

There are 1716 possible hands.

Since the order in which the two cards are picked up does not matter, you will need to to use combinations.

Combination Formula

A formula for the number of possible combinations of r objects from a set of n objects. This is written in any of the ways shown below.

So, from the problem above, it is 13C6, or (13! / 6! (13-6!):

13C6

13! / 6! (13-6!)

13! / (6! * 7!)

6227020800 / 720 * 5040

6227020800 / 3628800

1716