You select 3 cards randomly from a deck of 52 cards

Question

What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)?

Answer 1

Another way to do this problem is to use combinations to count the possibilities.

 

Assuming you are just pulling the 3 cards simultaneously (then taking a look):

 

The total possible number of outcomes is based on how many different combinations of 52 cards taken 3 at a tme there are: ₅₂C_3.

 

Since there are 12 face cards the number of "successful combos" you can pull is ₁₂C_3.

 

The probability of success: ₁₂C_{3 / 52}C_3. That calculation should give the same result as (12/52) (11/51) (10 /50)

Answer 2

If you putting the cards back in each time (with replacement)

 

There are 12 cards (4J , 4Q , and 4K)

 

(12/52)³= .012289

 

If the card is not replaced each time:

 

(12/52)(11/51)(10/50) = .009954