Transcript Find Probability

Five-Minute Check (over Lesson 8-1)
Main Idea and Vocabulary
Targeted TEKS
Example 1: Find a Permutation
Example 2: Use Permutation Notation
Example 3: Use Permutation Notation
Example 4: Find Probability
• Find the number of permutations of objects.
• permutation
Find a Permutation
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?
number of
possible
players
for first
base
10
x
number of
possible
players for
second
base
x
x
9
x
number of
possible
players for
third base
8
total
number of
= possible
ways
=
720
Answer: There are 720 different ways the manager can
pick players for first, second, and third base.
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?
A. 2,415
B. 2,730
C. 3,150
D. 3,375
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Use Permutation Notation
Find the value of P(7, 2).
P(7, 2) = 7 ● 6 or 42
Answer: 42
7 things taken 2 at a time
Find the value of P(8, 4).
A. 1,100
B. 1,375
0%
C. 1,420
D. 1,680
1.
2.
3.
4.
A
B
C
D
A
B
C
D
Use Permutation Notation
Find the value of P(13, 7).
P(13, 7) = 13 ● 12 ● 11 ● 10 ● 9 ● 8 ● 7
= 8,648,640
Answer: 8,648,640
13 things
taken 7 at a
time
Find the value of P(12, 5).
A. 72,110
0%
B. 84,800
C. 93,120
D. 95,040
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Find Probability
NUMBERS 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,
expressed as a percent, that one of these numbers
picked at random is an even number.
You are considering all permutations of 5 digits taken 5
at a time. You wish to find the probability that one of
these numbers picked at random is even.
Solve the Test Item
Find the number of possible five-digit numbers.
P(5, 5) = 5!
Find Probability
For a number to be even, the ones digit must be 2 or 4.
number of
ways to
pick the
last digit
2
x
x
number of
ways to
pick the first
four digits
P(4, 4)
=
=
number of
permutations
that are even
2P(4, 4) or 2 x 4 x 3 x 2 x 1
Find Probability
Substitute.
Divide out common
factors.
Simplify.
Answer: 40%
NUMBERS 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%
D. 60%
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D