Transcript Permutations - Skyline School

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Objective
Find the number of permutations of
objects
Vocabulary
Permutation
An arrangement or listing in which order is
important
Vocabulary
Factorial
The expression n! is the product of all counting
numbers beginning with n and counting
backward to 1
4! = 4 · 3 · 2 · 1
Math Symbols
P(a, b)
The number of permutations of a things taken b
at a time
Math Symbols
Factorial
!
5! Five factorial
5  4 3 2 1
Example 1 Use Permutation Notation
Example 2 Use Permutation Notation
Example 3 Find a Permutation
Find the value of
Write permutation
P(7, 2) =
P(7, 2) = 7  6
Answer:
P(7, 2) = 42
Since 1st number is the starting
number for the multiplication
The 2nd number determines
how many numbers to multiply
Multiply
1/3
Find the value of
Answer: P(8, 4) = 1,680
1/3
Find the value of
P(13, 7) =
Write permutation
P(13, 7) = 13  12  11  10  9  8  7
Answer:
P(13, 7) = 8,648,640
Since 1st number is the starting
number for the multiplication
The 2nd number determines
how many numbers to multiply
Multiply
2/3
Find the value of
Answer: P(12, 5) = 95,040
2/3
SOFTBALL There are 10 players on a softball team. In
how many ways can the manager choose three players
for first, second, and third base?
P(a, b) =
P(10,
The player chosen for first
cannot play at second or third
Permutation = order important
Write permutation formula
“a” represents the number of
choices
Replace a with 10
3/3
SOFTBALL There are 10 players on a softball team. In
how many ways can the manager choose three players
for first, second, and third base?
P(a, b) =
P(10, 3) =
P(10, 3) = 10 
“b” represents the number wants
to choose
Replace b with 3
Since a = 10, begin the
permutation with 10
A permutation is a modified
factorial which means to multiply
3/3
SOFTBALL There are 10 players on a softball team. In
how many ways can the manager choose three players
for first, second, and third base?
P(10, 3) =
b is the number of players
want to choose, so multiply
3 numbers counting down
from 10
P(10, 3) = 10  9  8
10  9  8
Answer:
P(10, 3) = 720 ways
Multiply
P(a, b) =
Add dimensional analysis
3/3
STUDENT COUNCIL There are 15 students on student
council. In how many ways can Mrs. Sommers choose
three students for president, vice president, and
secretary?
Answer: P(15, 3) = 2,730 ways
3/3
Assignment
Lesson 8:3
Permutations
4 - 26 All
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an even number
number.
A 20%
B 30%
C 40%
D 50%
P (even) = Possible numbers even
Write probability statement
Numerator is in probability
statement
4/4
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an even number
number.
A 20%
B 30%
C 40%
D 50%
P (even) = Possible numbers even
Total possible numbers
Denominator is “total
numbers possible”
P (even) = 2
2 & 4 are the only
even numbers
Replace numerator
with 2
4/4
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an even number.
P(A, B) = Possible outcomes
Write permutation
P(5, 5) = 5  4  3  2  1
5 digits taken 5 at a time
P(5, 5) = 120
P (even) =
P(5, 5) = 5!
Possible numbers even
120
4/4
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an even number.
Write permutation
P(A, B) = Possible outcomes
P(4, 4) = 4  3  2  1
P(4, 4) = 24
In order for a number
to be even, the ones
digit must be 2 or 4.
To write first 4
numbers of an even
5 digit number use
permutation
4/4
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an even number.
P(4, 4) = 24
An even number has to be
in the one’s digit
P(2, 1) = 2
Two digits are even so 2
digits taken 1 at a time
P(even) = 24  2
P(even) = 48
Now multiply the two
permutations together
4/4
Substitute.
P (even) =
48
120
P(5, 5) = 120
P(even) = 48
A 20%
B 30%
P (even) = 40%
Answer: C
C 40%
D 50%
Choices are in % so change
probability fraction to a % by
dividing numerator by
denominator then multiply
by 100
4/4
*
MULTIPLE-CHOICE TEST ITEM Consider all of the
five-digit numbers that can be formed using the digits
1, 2, 3, 4, and 5 where no digit is used twice. Find the
probability that one of these numbers picked at
random is an odd number.
A 30%
B 40%
C 50%
Answer: D
4/4
D 60%