Transcript Counting - University of New Mexico

Counting
Chapter 13 sec 1
Break
up into
groups
 One
method of counting is
using the tree diagram.
◦It is useful to keep track of
counting.
◦Order of permutations does
matter.
 You
will determine all the possible
ways to count.
 Remember order matters!!
 How
many ways can we do
each of the following?
◦Flip a coin?
◦2 ways; One head and one
tails.
Roll
a single die?
6 ways
 Pick
a card from a standard
deck of cards?
 52 ways
 Example;
How many ways can 3
coins be flipped?
◦How would you list the
ways?
◦How would you list the
possibilities?
 Make
a tree diagram
 1st
row is first coin
 2nd row is the second coin
 3rd row is the third coin.
 You
are listing out the
possibilities.
Begin

H
H
H
T
T
T
T
H
T
H
H
T
H
T
HHH, HHT, HTH, HTT, TTH, TTT, THH, THT
How
about rolling two
dice?
◦Let us say that one
die is red and the
other is green.
In
your group see if you
can find all combinations.
Starting with
◦(1,1), (1, 2), (1,3), …
◦36 ways.
 If
objects are allowed to be
used more than once in a
counting problem, we will use
the phrase with repetition.
 If
we do not want objects to be
used more than once, without
repetition.
 Draw
a tree diagram that
illustrates the different ways to
flip a dime, penny, quarter, and
nickel.
 1.
In how many ways can you get
exactly one head?
4
2.
In how many ways can
you get exactly two tails?
6
How many different
three-digit numbers can
you form using the digits
1, 2, 5, 7, 8, & 9 without
repetition?
 3.
120
 You
are a designer and has
designed different tops, pants,
and jackets to create outfits for a
runway show. Without repetition,
how many different outfits can
your models wear if you had
designed the following:
 Seven
tops, six pants, three
jackets.
126