Ice cream: A certain ice cream parlor offers twelve flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors. Part: 0/2 Part 1 of 2 In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle and which is on the bottom? The number of ways to choose a cone, if order matters, is Part: 1/2 Part 2 of 2 In how many ways can you choose a cone if the order of the flavors doesn't matter? The number of ways to choose a cone, if order doesn't matter, is Continue J X T 3 MacBook Air 5 Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 8 1 do P
Ice cream: A certain ice cream parlor offers twelve flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors. Part: 0/2 Part 1 of 2 In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle and which is on the bottom? The number of ways to choose a cone, if order matters, is Part: 1/2 Part 2 of 2 In how many ways can you choose a cone if the order of the flavors doesn't matter? The number of ways to choose a cone, if order doesn't matter, is Continue J X T 3 MacBook Air 5 Submit Assignment © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center | Accessibility 8 1 do P
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
![**Ice Cream Parlor Flavor Combinations**
A certain ice cream parlor offers twelve flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.
### Part 1 of 2
**Question:**
In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle, and which is on the bottom?
**Answer:**
The number of ways to choose a cone, if order matters, is [ ].
### Explanation:
To compute this, you would use permutations since the order in which you choose the flavors matters. The formula for permutations of \(n\) items taken \(r\) at a time is:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Here, \( n = 12 \) (since there are twelve flavors) and \( r = 3 \) (since we are choosing three scoops). Substituting these values into the formula gives:
\[ P(12, 3) = \frac{12!}{(12-3)!} = \frac{12!}{9!} = 12 \times 11 \times 10 \]
### Part 2 of 2
**Question:**
In how many ways can you choose a cone if the order of the flavors doesn't matter?
**Answer:**
The number of ways to choose a cone, if order doesn't matter, is [ ].
### Explanation:
To compute this, you would use combinations since the order in which you choose the flavors does not matter. The formula for combinations of \(n\) items taken \(r\) at a time is:
\[ C(n, r) = \frac{n!}{r!(n-r)!} \]
Here, \( n = 12 \) and \( r = 3 \). Substituting these values into the formula gives:
\[ C(12, 3) = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} \]
### Continue or Submit
At this point, you can either continue to another part of the assignment or submit your answers for this portion.
Remember to confirm your answers and verify your calculations before submission.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a07bd8-eb1c-498d-b0a8-9eb9d6fddf09%2F6e59be91-7c9d-4b37-a7d6-8783167f38ed%2F99c356s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Ice Cream Parlor Flavor Combinations**
A certain ice cream parlor offers twelve flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.
### Part 1 of 2
**Question:**
In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle, and which is on the bottom?
**Answer:**
The number of ways to choose a cone, if order matters, is [ ].
### Explanation:
To compute this, you would use permutations since the order in which you choose the flavors matters. The formula for permutations of \(n\) items taken \(r\) at a time is:
\[ P(n, r) = \frac{n!}{(n-r)!} \]
Here, \( n = 12 \) (since there are twelve flavors) and \( r = 3 \) (since we are choosing three scoops). Substituting these values into the formula gives:
\[ P(12, 3) = \frac{12!}{(12-3)!} = \frac{12!}{9!} = 12 \times 11 \times 10 \]
### Part 2 of 2
**Question:**
In how many ways can you choose a cone if the order of the flavors doesn't matter?
**Answer:**
The number of ways to choose a cone, if order doesn't matter, is [ ].
### Explanation:
To compute this, you would use combinations since the order in which you choose the flavors does not matter. The formula for combinations of \(n\) items taken \(r\) at a time is:
\[ C(n, r) = \frac{n!}{r!(n-r)!} \]
Here, \( n = 12 \) and \( r = 3 \). Substituting these values into the formula gives:
\[ C(12, 3) = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} \]
### Continue or Submit
At this point, you can either continue to another part of the assignment or submit your answers for this portion.
Remember to confirm your answers and verify your calculations before submission.
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