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
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
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![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b8f79a9-b6a4-48ca-ab39-5a4f4172185c%2F2c936e30-81eb-4cfa-aadb-311838d1fbbe%2Fr535jr9_processed.jpeg&w=3840&q=75)
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.
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