And we'll never be royals (ROYALS)
From a complete deck of cards (jokers not included) five cards are drawn to form a poker hand. The probability that the hand will be a royal flush is expressed as
wherein p and q are coprime. Find the last three digits of p + q.
Note: A hand is considered royal flush if if contains the cards 10, J, Q, K, and A all in the same suit.
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1 solution
P(royal flush)
= (1 royal 'family' per suit) × (4 suits per deck) / (52C5)
= 1 × 4 / (52!/5!47!)
= 4 / 2598960
= 1 / 649740
Answer = 1 + 740 = 741