__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__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__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__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__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__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 |

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**