Four cards are drawn at random from a pack of 52 playing cards Find the probability of getting all face cards?

Face cards in a regular set of playing cards consist of Jack, Queen, King, and Ace. With these 4 face cards occurring in all 4 suits (hearts, diamonds, clubs, and spades), that gives 16 total face cards.

If we draw 4 cards without putting them back, the probabilities are calculated on each draw as (number of face cards remaining)/(total number of cards remaining)

1st draw: 16/52 = 0.307692308

2nd draw: 15/51 = 0.294117647

3rd draw: 14/50 = .28

4th draw: 13/49 = 0.265306122

These are the individual probabilities of each step independent of each other. To calculate the probability when depending on the success of the previous step, we simply multiply each step's probabilities together.

Probability of drawing N face cards in a row:

1: (16/52) = 0.307692308

2: (16/52)*(15/51) = 0.0904977376

3: (16/52)*(15/51)*(14/50) = 0.0253393665

4: (16/52)*(15/51)*(14/50)*(13/49) = 0.00672268908

This translates to approximately a 7 in 1000 chance of drawing 4 face cards in a row out of a deck of 52 cards!