Answer
Decimal probability = 1.5391E-6
↓Steps Explained:↓

In a standard 5-card poker hand for 1 deck:
Calculate P(Royal Flush)
Royal Flush Hands
Calculate Total 5 Card hands
Choose 5 cards from 52 cards
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
Possible Royal Flushes = Possible ways to get 10,J,Q,K,A all suited
Possible Royal Flushes = 1 way * 4 possible suits (Spade,Heart,Diamond,Club) = 4
P(Royal Flush) = | Royal Flushes |
| Total Hands |
P(Royal Flush) = | 4 |
| 649,740 |
Reduce top and bottom by 4
GCF = Greatest Common Factor
P(Royal Flush) = | 4 |
| 2,598,960 |
GCF for 1 and 649740 = 4
P(Royal Flush) = | 1 |
| 649,740 |
Final Answer
Decimal probability =
1.5391E-6Related Calculators:
Hypergeometric Distribution |
Hardy-Weinberg |
Fishers Exact Test