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Answer
Success!
Decimal probability = 1.5391E-6

↓Steps Explained:↓

In a standard 5-card poker hand for 1 deck:

Calculate P(Royal Flush)

Royal Flush Hands

Ace of ClubsKing of ClubsQueen of ClubsJack of Clubs10 of Clubs
Ace of DiamondsKing of DiamondsQueen of DiamondsJack of Diamonds10 of Diamonds
Ace of HeartsKing of HeartsQueen of HeartsJack of Hearts10 of Hearts
Ace of SpadesKing of SpadesQueen of SpadesJack of Spades10 of Spades

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-6
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