10)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
10)
![### Lottery Combination Problem
In a certain lottery, players are required to select 6 different numbers from a range of 1 to 54, inclusive. The challenge is to determine how many different sets of 6 numbers can be chosen.
#### Task
Calculate the number of different ways to choose 6 numbers using the combination formula.
#### Formula
The number of combinations can be calculated using the formula for combinations:
\[
C(n, r) = \frac{n!}{r!(n-r)!}
\]
where:
- \( n \) is the total number of options (54 in this case),
- \( r \) is the number of selections to be made (6 in this case),
- \( ! \) denotes a factorial, which is the product of all positive integers up to that number.
#### Solution
Substitute \( n = 54 \) and \( r = 6 \) in the formula:
\[
C(54, 6) = \frac{54!}{6!(54-6)!}
\]
Calculate the result by simplifying the factorial expressions.
#### Final Step
Enter your simplified answer as an integer or a fraction in the provided space.
---
Remember that solving this requires an understanding of factorials and combinations, which are fundamental concepts in probability and combinatorics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faebb69bd-3f9d-42b2-82f4-ec61105a4478%2F454549f7-8f1b-4bb6-b746-5db0f66eeceb%2F5znmos_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Lottery Combination Problem
In a certain lottery, players are required to select 6 different numbers from a range of 1 to 54, inclusive. The challenge is to determine how many different sets of 6 numbers can be chosen.
#### Task
Calculate the number of different ways to choose 6 numbers using the combination formula.
#### Formula
The number of combinations can be calculated using the formula for combinations:
\[
C(n, r) = \frac{n!}{r!(n-r)!}
\]
where:
- \( n \) is the total number of options (54 in this case),
- \( r \) is the number of selections to be made (6 in this case),
- \( ! \) denotes a factorial, which is the product of all positive integers up to that number.
#### Solution
Substitute \( n = 54 \) and \( r = 6 \) in the formula:
\[
C(54, 6) = \frac{54!}{6!(54-6)!}
\]
Calculate the result by simplifying the factorial expressions.
#### Final Step
Enter your simplified answer as an integer or a fraction in the provided space.
---
Remember that solving this requires an understanding of factorials and combinations, which are fundamental concepts in probability and combinatorics.
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