Math 221 Counting Worksheet: Poker Hands A standard 52-card ...

Math 221 Counting Worksheet: Poker Hands
A standard 52-card deck consists of 13 cards from each of 4 suits (spades, hearts,
diamonds, clubs). The 13 cards have value 2 through 10, jack (J), queen (Q), king (K), or
ace (A). Each value is a “kind” of card. The jack, queen, and king are called “face
cards”.
How many 5-card poker hands are there?
How many contain a royal flush (10, J, Q, K, A all of the same suit)?
How many contain a straight flush (5 consecutive cards of the same suit)?
Do not include royal flushes in your count.
Note: For a straight, aces can be either high or low, e.g. A-2-3-4-5 and 10-J-Q-K-A are
valid straights but J-Q-K-A-2 is not.
How many contain four of a kind?
How many contain a full house (three of a kind plus a pair)?
How many contain a flush (5 cards of the same suit)? Do not include straight flushes or
royal flushes in your count.
How many contain a straight (5 consecutive cards)? Do not include straight flushes or
royal flushes in your count.

How many contain three of a kind (the other two cards are not a pair)?
How many contain two pairs (the two pairs must be of different “kinds”)?
How many contain exactly one pair?
How many contain just “high card” (none of the above)?