Transcript Squares and Square Roots

Permutations
Lesson 10 – 4
Vocabulary
• Permutation – an arrangement or listing of
objects in which order is important.
• Example: the first three classes of the day are
math, science, and history. How many ways
can you arrange your classes?
– To solve, think about how many choices are
possible for 1st Period?
– Then, how many choices are left for 2nd Period?
– How many choices left for 3rd period?
– Now, multiply, 3 x 2 x 1 = 6 arrangements.
Proof!
M – math
S – science
H – history
1st, 2nd, 3rd
MSH
SMH
HMS
MHS
SHM
HSM
Things to Know
# 1: How to recognize when it’s a
permutation and not combination?
Look for key words like; arranged, order,
how many ways, permutation, etc…
How many permutations are there from
using the letters in the word LETTERS?
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
Things to Know
# 2: Is there a symbol for permutation?
n! ‘the exclamation mark’
The ! means factorial. Factorial means to
multiply by the next smallest whole number
until you reach x 1.
Example: 5!
means to multiply 5 x 4 x 3 x 2 x 1 =
10!
means: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =
Things to Know
# 3: Can I stop before reaching 1?
If the question is asking for only a certain
amount, then ‘yes’.
Example: How many 3 digit outcomes be
formed from even digits, if no numbers can
be used more than once?
First, your digits to choose from: 2, 4, 6, 8
So, 1st digit: 4 choices; 2nd digit: 3 choices
3rd digit: 2 choices
Multiply 4 x 3 x 2 = 24 outcomes.
Practice
• How many 3 digit area codes can be
created if no digit repeats itself?
720 area codes
• 5 passengers are sitting in a car. How
many different seating arrangements can
there be?
120 seating arrangements
• There are 90 ways for two students to
become president and vice president of
student council. How many people were
in the election?
10 students
Practice
• You have five seasons of your favorite TV
show on DVD. If you randomly select two
of them from a shelf, what is the
probability that you will select season one
first and season two second?
1 / 20
• A password consists of four letters, of
which none are repeated. What is the
probability that a person could guess the
entire password by randomly selecting the
four letters?
1 / 358,800