Probability: drawing cards?

There are 13 x 4C3 ways of drawing 3 of a kind.

There are 12 x 4C2 ways of drawing 2 of a different kind.

The answer is just the product of those two.

13 x 4 x 12 x 6 = 3744

The total number of hands is 52C5 = 2598960

Divide that into 3744 to get 0.00144057623 probability.

That agrees with your second answer.

Your first answer is 0.01440576230

I'll have to think about your answers to see why they work. I think 5C3 represents the number of ways you can place the 3 of a kind, and 5C2 represents the number of ways you can place the 2 of a kind.

You can multiply out all the terms and it should agree with what I had above.

For what it's worth, I ran a million hand simulation and had a full house 1344 times.

5C3 is a shorthand way of writing 5!/3!(5 -3)! = [5*4*3*2*1]/[(1*2*3)*(1*2)] = 10

13 * (4C3) * 12 * (4C2)

= 13 * 4 * 12 * 6

=3744

3744/52C5 = 3744/2,598,960 = 1/694.166667