Calculating odds of flopping a pair

[AaronBrown]

First, 50 choose 3 is 19,600, not 15,180 (that's 46 choose 3, which does not help for this problem). Second, 5,676/15,180 is 37%, not 30%.

As fiskebent said, you've computed the probability of getting a pair and two cards that are not A or K (although they might form a pair between them).

To complete the problem, you can compute all the possibilities:

A or K/x/x 5,676
A/K/x 396
A/A/x or K/K/x 264
A/A/K or K/K/A 18
A/A/A or K/K/K 2

The total is 6,356. Divide by 19,600 to get 0.3243 or about 32%.