### First Problem

Two cards are selected from a deck of 52 cards. In how many different ways
this can be done so :
- they are same color
- they are different color
- they are a pair
- they are a pair of same color
- 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

- How many different poker hands can be dealt?
- How many different poker hands can be dealt if all are same color?
- How many different poker hands can be dealt if it must have both colors?
- How many different poker hands can be dealt if all are same suit?
- How many different poker hands can be dealt if it must include all suits?
- 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?
- 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

- A
__Royal Flush__ consists of a 5-card hand with A-K-Q-J-10 of the same suit.
How many are there?
- 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)
- A
**Straight Flush** consists of 5 cards in sequence in the same suit, but
doesn't include royal flush. How many are there?
- 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?
- 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

__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?
- A
__Full house__ consists of a pair (two of a kind) and three of a kind. How
many are there?
- 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?
__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?
__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)*