You're missing the combinations where you flop more than 1 A/K.

I think it's easier to solve it if you look at the odds of missing. There are C(44,3) combinations that miss you completely and C(50,3) combinations in all. The chance of missing is C(44,3)/C(50,3). So the chance of hitting in some way is 1-C(44,3)/C(50,3) or ~32.4%.

Hope that helps.