lesson 2 menu
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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. Lesson 2 Menu. Find the number of permutations of objects. permutation. - PowerPoint PPT PresentationTRANSCRIPT
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 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?
Answer: There are 720 different ways the manager can pick players for first, second, and third base.
10 9 8 720x x =
number of possible players for first base
number of possible
players for second base
number of possible
players for third base
total number of possible
waysx x =
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 2,415
B. 2,730
C. 3,150
D. 3,375
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?
Use Permutation Notation
Find the value of P(7, 2).
P(7, 2) = 7 ● 6 or 42 7 things taken 2 at a time
Answer: 42
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 1,100
B. 1,375
C. 1,420
D. 1,680
Find the value of P(8, 4).
Use Permutation Notation
Find the value of P(13, 7).
P(13, 7) = 13 ● 12 ● 11 ● 10 ● 9 ● 8 ● 7 13 thingstaken 7 at
atime
= 8,648,640
Answer: 8,648,640
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 72,110
B. 84,800
C. 93,120
D. 95,040
Find the value of P(12, 5).
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 ItemFind 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.
Find Probability
number of ways to pick the last digit
number of ways to pick the first four
digits
number of permutations that are even
x =
2 x P(4, 4) = 2P(4, 4) or 2 x 4 x 3 x 2 x 1
Answer: 40%
Find Probability
Substitute.
Divide out common factors.
Simplify.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 30%
B. 40%
C. 50%
D. 60%
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.