# Math Help - calculating probability for getting specific cards

1. ## calculating probability for getting specific cards

Hello,

I need to calculate some probabilities in poker and one of the situtations goes like this:
I've already gotten two cards for example Ace and King and I want to calculate the probability of getting a Queen, Jack and 10 in the next three drawn cards. I want to ignore that there might be other players at the table at this time.

I thought that you do it like this:
$
\frac{12}{50} + \frac{8}{49} + \frac{4}{48}
$

Is that correct?

My given assignment states that I need to use combinatorics / permutations to solve it, and I’m not sure how I do this.

I think what I need to do is calculate how many different combinations there is for drawing the three cards I want and then divide that by the number of total combinations there are for drawing 3 random cards. Like this:

$
\frac{50!}{3!(50-3)!} = 19600
$

$
\frac{12 * 8 * 4}{19600}
$

There is a problem here however, when doing 12*8*4 you calculate all the possibilites for drawing the three cards where the order they are drawn matter but the order of how the cards are drawn doesn't matter.

However this result is not the same as the first one? So which method is correct and what am I doing wrong?

I hope someone can help me with this
Thanks alot
Jacob

2. If the order doesn't matters I think it should be:

(4*4*4)/ 50C3

because you have 4 Queens and it will be taken 1, you have 4 Jacks and it will be taken 1 and you have 4 cards 10 and it will be taken 1.

the number of possibilities is 50C3 because the order doesn't matter (so it is a combination) and you have 50 cards and you will take 3.

3. Originally Posted by azarat
Hello,

I need to calculate some probabilities in poker and one of the situtations goes like this:
I've already gotten two cards for example Ace and King and I want to calculate the probability of getting a Queen, Jack and 10 in the next three drawn cards. I want to ignore that there might be other players at the table at this time.

I thought that you do it like this:
$
\frac{12}{50} + \frac{8}{49} + \frac{4}{48}
$

Is that correct?

My given assignment states that I need to use combinatorics / permutations to solve it, and I’m not sure how I do this.

I think what I need to do is calculate how many different combinations there is for drawing the three cards I want and then divide that by the number of total combinations there are for drawing 3 random cards. Like this:
Try this:
$\frac{\displaystyle{\binom{4}{1}\binom{4}{1}\binom {4}{1}}}{\displaystyle\binom{50}{3}}$