Stay with me! because I'm not very good with maths but I've been trying.

Ok so I know from a formula I don't quite understand that the probability of these flops are:

A high = 21.7
K high = 18.3
Q high = 15.2 etc

However I want to know the probability of the first two cards

AA high
AK high
AQ high as it were.

I understand the difference between combinations and permutations. I know and understand that FACT(52)/(FACT(3)*FACT(52-3)) gives 22100 different flops where order does not matter.

I thought I would work out the probability of each flop and add them up for example AKK + AKQ + AKJ... would equal AK high flop.

Instinctively I did 4/52 * 4/51 * 4/50 for AKQ etc but I guess that would be one permutation so I multiplied by 6 (the different ways to arrange 3 cards) = .29%

Anyway after doing all this I summed up all AA, AK, AQ... which should equal 21.7% the probability of A high flop but I got 24.4%

Can anyone make sense of my none sense? And sorry if I'm bothering anyone with my ridiculousness.

Make sure you adjust the number of permutations for paired and trip flops.

AAA has 1 permutation (AAA).

AAX has 3 permutations (AAX/AXA/XAA).

AKX has 6 permutations (AKX/AXK/KAX/KXA/XAK/XKA).

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Example 1: Probability of flopping AAX in any order:

1st card: 4/52
2nd card: 3/51
3rd card: 48/50
Permutations: 3

4/52 * 3/51 * 48/50 * 3 = 1.3%

Example 2: Probability of flopping AKX in any order:

1st card: 4/52
2nd card: 4/51
3rd card: 46/50
Permutations: 6

4/52 * 4/51 * 48/50 * 6 = 3.3%

I recommend using combinations rather than permutations, so you don't have to worry about order. Here are several examples showing the number of possible flops of the specified type:

Flop 1 Ace. C(48,2)*C(4,1)

Flop 0 Broadway. C(32,3)

Flop Monotone. C(13,3)*C(4,3)

For this last example, the first term is the number of ways to select 3 of 13 ranks and the second term is the number of ways of selecting 3 different suits.