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Math of the Demon Duck

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Ertxiem:
Well, actually, I asked for the probability of having 3 of a kind. This is 0.02113... or about 3 in 142. Yeah... I knew the answer... sorry...

A poker (4 of a kind) is not included, so it should also be considered. Furthermore, you missed ABCAB in the two pairs cases.

How to compute itI use combinations: nCp = n! / ( p! (n-p)! ) ,  that give the number of different choices of p elements from a set of n elements when the order is not relevant.
And the factorial n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1 .

So, the probability is the product of:
4C3 = 4 -> The number of sets of 3 suits we can have in our hand
13C1 = 13 -> The number of different values we can have in the trio
4C1 = 4 -> The number of sets of 1 suits we can have in our hand
4C1 = 4 -> The number of sets of 1 suits we can have in our hand (this term appears twice)
12C2 = 66 -> The number of sets of 2 values we can have in our hand

And this divided by
52C5 = 2 598 960 -> The number of sets of 5 cards we can have in our hand (from 52 cards in a deck).

So, the probability p is given by
p =  4C3 * 13C1 * 4C1 * 4C1 * 12C2  /  52C5

p = 4 * 13 * 4 * 4 * 66  /  2 598 960

p ≈ 0.02113

Regarding the line, you're right, I meant curve (like the Peano curve, a fractal).

And about algebra... weren't you called a long time ago Algebra15 and latter (after your PC was stricken by lightning) Algebra17?

ArtDrake:
Yes, I was. And I did figure out that I missed one. And also, in poker, you're allowed to count higher hands as lower hands (if only for the sake of rubbing it in; I personally like to say, when everyone else has a poor hand, and I have 4 of a kind, "two pair -- jacks and jacks" or something like that).

Deagonx:
What is the mathematical notation for the square route of negative 1? (-1)

ArtDrake:
The square root? That would be

The square route would be a two-block journey to 1 + 0i.

Tastidian:
Osirus dont take this the wrong way but why did you start this tread?

Also I would just like to know what is in store for me. Is there any way you can define the difficulty of calculus to me.

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