How many of each hand are there in a deck?
Poker Combinations
and our pre-test
I Win by flickr user Kevin Labianco

(5) In a 52 card deck, how many 5 card poker hands are possible that
have exactly two pair?
one pair?

Poker Combinations
Given a standard deck of 52 cards, how many ways are there to
draw 5 cards to obtain each hand.
(a) Royal Flush
[ace, king, queen, jack, ten in the same suit]

(b) Straight flush
[five cards in sequence and of the same suit, but not ace king queen
jack ten]

(c) Four of a kind
[four cards of one face value and one other card]

(d) Full house
[3 cards of one face value and 2 cards of another face value]

(e) Flush
[5 cards of the same suit but not in sequence, not including the
straight flush and royal flush above]

(f) Straight
[5 cards in sequence, but not all of same suit. Ace high or low]

(g) Three of a Kind
[exactly 3 cards of one face value and 2 different cards]

(h) Two pairs
[one pair of each two different face values and a card of a third
face value]

(i) One pair
[two of one face value, and 3 cards of different face values, no
matching the pair]

(j) No pairs
[5 different face values, not in sequence, not all cards in the same suit]

How many different necklaces of 12 beads each can be
made from 18 beads of different colours?
EXTRA PRACTICE
ENJOY!

(a) The last part of your telephone number contains four digits.
How many such four-digit numbers are there?
b) How many such four-digit numbers are there if the same
digit cannot be used twice?
c) How many four-digit numbers begin with a 2 ,4 or 0 if the
same digit cannot be used twice?

In how many ways can the student council choose a subcommittee
of 5 people from the entire council which consists of 11 people?

(a) How many 3-digit numbers can be formed if no digit is used more
than twice in the same number?
(b) How many of these numbers are odd?
(c) How many of these numbers are divisable by 5?

(a) How many different 4 digit numbers are there in which all the
digits are different?
(b) How many of these numbers are odd?
(c) How many of these numbers are divisable by 5?

A 120-room hotel has reservations from 6 guests for 6
different rooms. In how many ways can the rooms be
assigned?

How many ways can the batting order of a 9-member
softball team be listed?

A nickel and a quarter and a dime are tossed on a table. Create a
tree diagram to determine how many ways these coins can land
on the table. (The order in which the coins land doesn't matter; it
will next week.)