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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
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.
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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