MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
![**Question:**
There are 10 students participating in a spelling bee. In how many ways can the students who go first and second be chosen?
**Options:**
- a) 1
- b) 90
- c) 3,628,800
- d) 45
**Explanation:**
To find the number of ways to choose the students who go first and second in the spelling bee, we need to consider the number of permutations of 10 students taken 2 at a time.
The formula for permutations is given by:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Where \( n \) is the total number of items (students, in this case), and \( r \) is the number of items to choose (first and second places).
For this problem:
\[ n = 10 \]
\[ r = 2 \]
Thus:
\[ P(10, 2) = \frac{10!}{(10-2)!} = \frac{10!}{8!} \]
\[ 10! = 10 \times 9 \times 8! \]
\[ \frac{10!}{8!} = 10 \times 9 = 90 \]
So, the number of ways to choose the students who go first and second is \( \boxed{90} \).
Hence, the correct answer is b) 90.](https://content.bartleby.com/qna-images/question/3b8f79a9-b6a4-48ca-ab39-5a4f4172185c/2c936e30-81eb-4cfa-aadb-311838d1fbbe/r535jr9_processed.jpeg)
Transcribed Image Text:**Question:**
There are 10 students participating in a spelling bee. In how many ways can the students who go first and second be chosen?
**Options:**
- a) 1
- b) 90
- c) 3,628,800
- d) 45
**Explanation:**
To find the number of ways to choose the students who go first and second in the spelling bee, we need to consider the number of permutations of 10 students taken 2 at a time.
The formula for permutations is given by:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Where \( n \) is the total number of items (students, in this case), and \( r \) is the number of items to choose (first and second places).
For this problem:
\[ n = 10 \]
\[ r = 2 \]
Thus:
\[ P(10, 2) = \frac{10!}{(10-2)!} = \frac{10!}{8!} \]
\[ 10! = 10 \times 9 \times 8! \]
\[ \frac{10!}{8!} = 10 \times 9 = 90 \]
So, the number of ways to choose the students who go first and second is \( \boxed{90} \).
Hence, the correct answer is b) 90.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 2 images
Knowledge Booster
Similar questions
- Getting at least one head when tossing three fair coins.arrow_forwardThirteen people work in an office. If eight of them are to be chosen to serve on a hiring committee, how many ways can this committee be chosen? a. 1287 b. 51,891,840 c. 5,040 d. 8arrow_forwardHow many different arrangements of gold, silver and bronze medalists can be made from 8 sprinters in the 100 meter Olympic final? Select one: O a. 6 O b. 512 O c. 56 O d. 336 OO Clear my choicearrow_forward
- ??arrow_forwardHow many different ways can a race with 5 runners be completed? (Assume there is no tie.) Your answer is: Question Help: D Video D Post to forumarrow_forwardC Clever | Teacher Page C Clever | Teacher Page Math To Do, i-Ready A login.iready.com/student/dashboard/home Tina Diana makes 3 batches of biscuits using 15 cups of flour. How many cups of flour does Diana use per batch? Use the number pad to enter your answer in the box. cups 3 O of 5 Completed 2)arrow_forward
- 198 students wear pretty costumes, 93 students wear traditional costumes. About how many students plan to wear a pretty or traditional costume?arrow_forwardSixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The incomplete) results are shown in the table below. Fill in the blanks for the table. a b d e f garrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman