First Problem

Two cards are selected from a deck of 52 cards. In how many different ways this can be done so :
  1. they are same color
  2. they are different color
  3. they are a pair
  4. they are a pair of same color
  5. they are a pair of different color
Answers (not in order): (24), (650), (26), (78), (52), (325), (676)

The following problems are about the poker hand which consists of 5 cards selected at random from an ordinary deck.

Second Problem

  1. How many different poker hands can be dealt?
  2. How many different poker hands can be dealt if all are same color?
  3. How many different poker hands can be dealt if it must have both colors?
  4. How many different poker hands can be dealt if all are same suit?
  5. How many different poker hands can be dealt if it must include all suits?
  6. How many different poker hands can be dealt if exactly one must be a King and the others of the same suit as the king?
  7. How many different poker hands can be dealt if exactly one must be a King and the others of the same color as the king?
Answers (not in order): (11440), (2467400), (1980), (5148), (2598960), (59800), (131560), (202400), (685464), (42504)

See the following Image

Third Problem

  1. A Royal Flush consists of a 5-card hand with A-K-Q-J-10 of the same suit. How many are there?
  2. How many poker hands contains 5 consecutive cards of the same suit (Assume that an Ace can be used either high or low; that is both A-K-Q- J-10 or 5-4-3-2-A)
  3. A Straight Flush consists of 5 cards in sequence in the same suit, but doesn't include royal flush. How many are there?
  4. A Flush is a 5-card hand in which all cards are the same suit, but not all in sequence (not a straight flush nor a royal flush). How many are there?
  5. A Straight is any 5 cards in sequence, but not in the same suit. How many are there?
Answers (not in order): (10200) , (36) , (5108) , (4), (40)

Fourth Problem

  1. Four-of-a-kind is a 5-card hand in which 4 of the cards are the same denomination, such as 4 kings, 4 queens or 4 aces. How many are there?
  2. A Full house consists of a pair (two of a kind) and three of a kind. How many are there?
  3. A Pair is a 5-card hand in which just 2 of the cards are the same denomination and the others are not, such as Q-Q-5-4-2. How many are there?
  4. Three-of-a-kind consists of a 5-cards hand in which 3 of the cards are the same denomination and the other 2 cards are not, such as K-K-K-4-5. How many are there?
  5. Two pairs is a 5-cards hand with 2 sets of 2 of a kind and the fifth card that doesn't match the others, such as Q-Q-5-5-A. How many are there?
Answers (not in order): (54912) , (123552) , (3744) , (624) , (1098240)

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