Do Now: Make a tree diagram that shows the
number of different objects that can be created.

T-shirts: Sizes: S, M, L and
Type: long sleeved and short sleeved
Academy Algebra II/Trig
14.1: Counting,
14.2: Permutations and Combinations
HW: tonight-p.978(22-24, 26),p.986(31, 34-36)
HW: Monday: p.986-987 (38-62 even)
Quiz 14.1, 14.2: Wednesday: 11/6
Fundamental Counting Principle
one event occurs m ways & another event
occurs n ways, then both events occur
ways.
 If
 You
have 3 shirts, 4 pairs of pants, and 2
pairs of shoes. How many outfits can you
create?
Fundamental Counting Principle
 How
many different license plates are
possible if you have 1 letter followed by 2
digits followed by 3 letters if letters and
digits can repeat?
 How
many plates are possible if letters and
digits cannot repeat?
Permutations
 An
ordering of n objects is a
permutation of the objects. (Order is
important)
 The
number of permutations of n
objects is n!.
Permutations

The number of permutations of r objects taken
from a group of n distinct objects is denoted by
, n = total # of objects, r = how many you
are taking.
can also be written as
.

We will use the calculator to get these answers
– from HOME screen, go to MATH menu (2nd 5)
and select probability – nPr.
Permutations
 10
people are in a race.
– How many different ways can the people
finish in the race?
– How many different ways can 3 people
win 1st, 2nd, and 3rd place?
Permutations
 p.981
ex 3: In how many ways can 5
people be lined up?
Permutations
 P.982
ex 5: All we know about Shannon,
Patrick, and Ryan is that they have
different birthdays. If we listed all the
possible ways this could occur, how
many would there be? (Assume there
are 365 days in a year.)
Permutations with Repetition
number of permutations of n objects
where an object repeats s # of times.
 The
Find the number of distinguishable
permutations of the letters in the word.
1.) WYNES
2.) TALLAHASSEE
3.) MATAWAN
Combinations
ordering of r objects from a total of
n objects where order is not important
is a combination.
 An
Combinations

The number of combinations of r objects taken
from a group of n distinct objects is denoted by
, n = total # of objects, r = how many you
are taking.

We will use the calculator to get these answers
– from HOME screen, go to MATH menu (2nd 5)
and select probability – nCr.
Combination or Permutation
 P.984
ex 8: How many different
committees of 3 people can be formed
from a pool of 7 people?
Combination or Permutation
 P.984
ex 9: In how many ways can a
committee of 2 faculty members and 3
students be formed if 6 faculty members
and 10 students are eligible?
A
Combination or Permutation
club has a president and vice-president
position. Out of 12 students, how many
ways can students be chosen for these
two positions?
A
Combination or Permutation
relay race has a team of 4 runners who
run different parts of the race. There are
20 students on your track squad. In how
many ways can the coach select students
to compete on the relay team?
Combination or Permutation
 P.987
#53: An urn contains 7 white balls
and 3 red balls. Three balls are selected.
In how many ways can the 3 balls be
drawn from the total of 10 balls:
– If 2 balls are white and 1 is red?
– If all 3 balls are white?
– If at least 2 balls are red?**
Combination or Permutation
 P.987
#59: A baseball team has 15
members. Four of the players are
pitchers, and the remaining 11 members
can play any position. How many different
teams of 9 players can be formed?
From a standard 52-card deck, find the
number of 5-card hands that contain the
cards specified.
1.) 5 of any card
2.) 5 face cards
From a standard 52-card deck, find the
number of 5-card hands that contain the
cards specified.
3.) 5 cards of the same color
4.) 1 ace and 4 cards that are not aces
From a standard 52-card deck, find the
number of 5-card hands that contain the
cards specified.
5.) 5 clubs or 5 spades
6.) at most 1 queen