Two cards are chosen at random from a standard 52-card deck. What is the probability that both cards are numbers (2 through 10) totaling to

I'll give this one a shot......we have the following combos as possibilites

(2,10)  (3,9) (4,8) (5,7) (6,6)

In the first four cases we have 16 ways to form each .....choose any one of four cards from the first given rank and choose the same from the second one. So C(4,1) * C(4,1) = 16

In the last case we just want to choose any two of the four "6s" and there are C(4.2) ways to do that = 6 ways

So, the total possibilities  = 16*4 + 6 = 70

And the total possibilities from choosing any 2 cards from 52 = C(52, 2)   = 1326

So.....  70 / 1326 =  about .053 = about 5.3% 

Someone else needs to check this, since I'm never sure about these "counting" problems  !!!

yep, this is correct. Totally makes sense.