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In: Advanced Math

Problem 3. A standard deck of cards contains 52 cards: 13 Ranks: A,2,3,4,5,6,7,8,9,10,J,Q,K 4 Suits: Clubs,...

Problem 3. A standard deck of cards contains 52 cards:

13 Ranks: A,2,3,4,5,6,7,8,9,10,J,Q,K
4 Suits: Clubs, Diamonds, Hearts, Spades

Suppose you draw a hand of 5 cards from the deck. Consider the following possible hands of cards. For each part, explain how you derive your solutions.

3(a) How many different hands of 5 cards exist?

3(b) How many ways can you draw a single pair? A single pair means that there are exactly two cards with the same rank (no additional pairs and no 3 of a kind, etc.).

3(c) How many ways can you draw 4 of a kind? (4 cards of the same rank)

3(d) How many ways can you draw a full house? A full house is a pair of one rank and three cards of another rank.

3(e) How many ways can you draw a straight? A straight is 5 consecutive ranks. The Ace (A) can either go before 2 or after K.
E.g., A,2,3,4,5 and 10,J,Q,K,A are both valid, as are 4,5,6,7,8 and 7,8,9,10,J etc.

Note: if you were to divide the number of hands of a particular type by the total number of 5 card hands, you would achieve the probability (odds) of randomly drawing a hand of that type.

Solutions

Expert Solution

Colby Messinger answered 2 years ago
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