There are 10 students participating in a spelling bee. In how many ways can the students who go first and second be chosen? O a C d 1 90 3,628,800 45

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
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.
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
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman