Probability of Choose Your Hand

                   

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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