Poker Hand: Probability that Five Cards are of the Same Suit

Problem
In a 5-card poker hand, what is the probability that all 5 are of the same suit?
 

Solution

 

Information
In poker hand, cards of the same suit and in any order is called Flush. Example of flush is (2♦, 5♦, 6♦, 9♦, Q♦ ~ a diamond flush). A flush whose cards are in sequence (i.e. 4♣, 5♣, 6♣, 7♣, 8♣) is called Straight Flush. A straight flush whose cards are composed of (10, J, Q, K, Ace) is called Royal Flush. Example of royal flush is (10♥, J♥, Q♥, K♥, A♥). Royal flush is the best possible hand in poker.
 

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