Question

Suppose you deal three cards from a regular deck of 52 cards, What is the probability that they will all be jacks?

Answer 1

Since there are 4 Jacks in the deck and 52 cards, the first time you draw a card the chances are 4/52 that you will draw a Jack.  Now that you have drawn a Jack, there are only 3 left in the deck so now the probability of drawing another Jack is 3/52.  The next Jack will be 2/52.  To get the probability that this will happen, we multiply the 3 fractions together...

4/52 * 3/52 * 2/52 = 24/140,608 = .00017 or .017%

Answer 2

Answer:

$0.00018$

Step-by-step explanation:

The number of ways you can draw 3 cards from the deck of 52 cards is,

$\dbinom{52}{3}=\dfrac{52!}{3!\ 49!}=\dfrac{52\times 51\times 50}{6}=22100$

Out of 52, 4 cards are jacks. So the number of ways you can draw 3 jacks out of 4 is,

$\dbinom{4}{3}=\dfrac{4!}{3!\ 1!}=\dfrac{24}{6}=4$

So, the probability three cards from a regular deck of 52 cards will be,

$\dfrac{4}{22100}=0.00018$