# Thread: Permutations involving playing cards

1. ## Permutations involving playing cards

Hi I have been given this question:

Three cards are picked without replacement from a shuffled standard pack of 52 playing cards. What is the probability of picking an ace followed by 2 hearts?

My attempt: Let omega be a set of ordered sequences of 3 cards drawn without replacement
|omega|=52x51x50

Let A be the event of picking an ace followed by 2 hearts
A=(ace of hearts, heart, heart)+(ace but not ace of hearts, heart, heart)
How do I calculate |A|?

2. ## Re: Permutations involving playing cards

Originally Posted by yellowcarrotz
Three cards are picked without replacement from a shuffled standard pack of 52 playing cards. What is the probability of picking an ace followed by 2 hearts?
My attempt: Let omega be a set of ordered sequences of 3 cards drawn without replacement
|omega|=52x51x50
Let A be the event of picking an ace followed by 2 hearts
A=(ace of hearts, heart, heart)+(ace but not ace of hearts, heart, heart) How do I calculate |A|?
I will help the one if you do the other and add together.
$\mathcal{P}(\text{ace of hearts, heart, heart})=\frac{(1)(12\cdot 11)}{52\cdot 51\cdot 50}$

3. ## Re: Permutations involving playing cards

thanks got it