I think you need to check your math.
For 13 coin flips, there are 16,384 possible outcomes. Of those, in 572 (or about 3.5%) there will be 10 heads.
The correct formula is N!/X!(N-X).
13!/(10!*3) = (13*12*11/3) = 572
Regardless, this has no impact on the probability of an independent coin toss.