Probability of Choose Your Hand




Calculate the probability of drawing a AKKQJ

First calculate the total number of possible hands in a 52 card deck:
From a deck of 52 cards, we want the number of possible unique ways we can choose 5 cards.
Using the combinations formula 52 choose 5 shown here, we get:
Total Possible 5 Card Hands =52!
(52-5)! * 5!

Total Possible 5 Card Hands =52!
47! * 5!

Total Possible 5 Card Hands =(52 * 51 * 50 * 49 * 48) * 47!
47! * (5 * 4 * 3 * 2 * 1)

Cancelling the 47! on top and bottom we get:
Total Possible 5 Card Hands =311,875,200
120

Total Possible 5 Card Hands = 2,598,960

Calculate the probability of drawing Ace
Ace
There are 4 A cards in the deck and 52 total cards in the deck to choose from
Probability of drawing A =4
52

Calculate the probability of drawing King
King
There are 4 K cards in the deck and 51 total cards in the deck to choose from
Probability of drawing K =4
51

Calculate the probability of drawing King
King
There are 3 K cards in the deck and 50 total cards in the deck to choose from
Probability of drawing K =3
50

Calculate the probability of drawing Queen
Queen
There are 4 Q cards in the deck and 49 total cards in the deck to choose from
Probability of drawing Q =4
49

Calculate the probability of drawing Jack
Jack
There are 4 J cards in the deck and 48 total cards in the deck to choose from
Probability of drawing J =4
48

Calculate final probability:
Since each card draw is independent, we multiply each of our 5 card draws
P(AKKQJ) =4 x 4 x 3 x 4 x 4
52 x 51 x 50 x 49 x 48

P(AKKQJ) =768
311875200

Probability(Choose Your Hand) =768
311,875,200

Using our GCF Calculator, we see that 768 and 311875200 can be reduced by 384
Reducing top and bottom by 384, we get:
Probability(Choose Your Hand) =2
812,175

In decimal format, this probability is equal to approximately 2.4625E-6