Calculating odds of flopping a pair

[AaronBrown]

Thanks for the kind words. Here they all are:

A or K/x/x 5,676

There are six cards that are A or K and 44 cards that are neither. 6*44*43/2 = 5,676. You have to divide by two because the last two cards are indistinguishable. This is the trickiest part of these calculations.

A/K/x 396

There are three Aces, three Kings and 44 other cards. 3*3*44 = 396.

A/A/x or K/K/x 264

3*2/2 = 3 ways to select two Aces out of three available, 44 ways to select x. 3*44 = 132. Double it for the K/K/x combinations to get 264.

A/A/K or K/K/A 18

3 ways to select the Aces, three ways to select one King out of three. 3*3 is 9. Double it for K/K/A to get 18.

A/A/A or K/K/K 2

One way to select three Aces, one way to select three Kings. 1 + 1 = 2.