In a standard 5-card poker hand for 1 deck:
Calculate P(Choose Your Hand)
Choose Your Hand Hands
Calculate the probability of drawing a TARGETHEARTRATEOFAGE67
Calculate Total 5 Card hands
| Total Hands = | 52! |
| (52-5)! * 5! |
| Total Hands = | 52! |
| 47! * 5! |
| Total Hands = | (52 * 51 * 50 * 49 * 48) * 47! |
| 47! * (5 * 4 * 3 * 2 * 1) |
Cancelling the 47!, we get:
| Total Hands = | 311,875,200 |
| 120 |
Total Hands = 2,598,960
Build Probability
Calculate the probabilty of each card
Calculate the probability of drawing Ace
There are 4 A cards in the deck
There are 52 total cards in the deck
| Probability of drawing A = | 4 |
| 52 |
Calculate the probabilty of each card
Calculate the probability of drawing Ace
There are 3 A cards in the deck
There are 51 total cards in the deck
| Probability of drawing A = | 3 |
| 51 |
Calculate the probabilty of each card
Calculate the probability of drawing Ace
There are 2 A cards in the deck
There are 50 total cards in the deck
| Probability of drawing A = | 2 |
| 50 |
Calculate the probabilty of each card
Calculate the probability of drawing Ace
There are 1 A cards in the deck
There are 49 total cards in the deck
| Probability of drawing A = | 1 |
| 49 |
Calculate the probabilty of each card
Calculate the probability of drawing 7
There are 4 7 cards in the deck
There are 48 total cards in the deck
| Probability of drawing 7 = | 4 |
| 48 |
Calculate the probabilty of each card
Calculate the probability of drawing 6
There are 4 6 cards in the deck
There are 47 total cards in the deck
| Probability of drawing 6 = | 4 |
| 47 |
Calculate final probability:
Since each card draw is independent
Multiply each of our 6 card draws
| P(TARGETHEARTRATEOFAGE67) = | 4 x 3 x 2 x 1 x 4 x 4 |
| 52 x 51 x 50 x 49 x 48 x 47 |
| P(TARGETHEARTRATEOFAGE67) = | 384 |
| 14658134400 |
Reduce top and bottom by 384
GCF = Greatest Common Factor
| P(Choose Your Hand) = | 384 |
| 14,658,134,400 |
GCF for 1 and 38172225 = 384
| P(Choose Your Hand) = | 1 |
| 38,172,225 |
