Probability Of Drawing Cards Calculator

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

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