Hello, algorith!

Your afterthought is correct . . .

What is the probability that a five-card poker hand has the following?

(a) Two Pairs (not four of a kind or a full house).

Choose a kind - 13

Choose 2 of a kind - C(4,2)

Choose another kind - 12

Choose 2 of a kind - C(4,2)

Choose last card - 44

Multiply all number above for answer.

Is that right?

Another thing that came to mind is to replace the 13 and the 12 by C(13,2),

I'm having trouble choosing one over the other. . This one is correct.

Can somebody confirm the right answer and explain why?

We choose 2 values from the possible 13 values: . ways.

. . (The order doesmatter.)not

Choose a pair: . ways.

Choose another pair: . ways.

Choose the fifth card: . ways.

So there are: .

There are: . possible 5-card hands.

Therefore: .