Underground sells only sandwiches. They offer three choices of bread, five types of meat toppings, five types of cheese and six vegetable toppings. If you must choose exactly one type of bread, one meat, one type of cheese and one vegetable for your sandwich, how many different kinds of sandwiches can you order at Underground?
Underground sells only sandwiches. They offer three choices of bread, five types of meat toppings, five types of cheese and six vegetable toppings. If you must choose exactly one type of bread, one meat, one type of cheese and one vegetable for your sandwich, how many different kinds of sandwiches can you order at Underground?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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![**Combinatorics in Sandwich Selection**
**Problem Statement:**
Underground sells only sandwiches. They offer three choices of bread, five types of meat toppings, five types of cheese, and six vegetable toppings. If you must choose exactly one type of bread, one meat, one type of cheese, and one vegetable for your sandwich, how many different kinds of sandwiches can you order at Underground?
**Explanation:**
To determine the total number of different kinds of sandwiches you can create, multiply the number of options for each category (bread, meat, cheese, and vegetable).
1. **Bread Choices:**
- 3 types of bread
2. **Meat Topping Choices:**
- 5 types of meat toppings
3. **Cheese Choices:**
- 5 types of cheese
4. **Vegetable Topping Choices:**
- 6 types of vegetable toppings
The formula to find the total number of different sandwiches is:
\[ \text{Total Sandwiches} = (\text{Number of Bread Choices}) \times (\text{Number of Meat Choices}) \times (\text{Number of Cheese Choices}) \times (\text{Number of Vegetable Choices}) \]
Substitute the given numbers into the formula:
\[ \text{Total Sandwiches} = 3 \times 5 \times 5 \times 6 \]
Finally, compute the total:
\[ \text{Total Sandwiches} = 3 \times 5 \times 5 \times 6 = 450 \]
**Conclusion:**
You can order 450 different kinds of sandwiches at Underground.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a3586c7-75e0-478e-8b93-fa570f1e3b86%2F69aee782-e4d1-4b1d-9a34-5a76bab92f2f%2Fcc2o7u_processed.png&w=3840&q=75)
Transcribed Image Text:**Combinatorics in Sandwich Selection**
**Problem Statement:**
Underground sells only sandwiches. They offer three choices of bread, five types of meat toppings, five types of cheese, and six vegetable toppings. If you must choose exactly one type of bread, one meat, one type of cheese, and one vegetable for your sandwich, how many different kinds of sandwiches can you order at Underground?
**Explanation:**
To determine the total number of different kinds of sandwiches you can create, multiply the number of options for each category (bread, meat, cheese, and vegetable).
1. **Bread Choices:**
- 3 types of bread
2. **Meat Topping Choices:**
- 5 types of meat toppings
3. **Cheese Choices:**
- 5 types of cheese
4. **Vegetable Topping Choices:**
- 6 types of vegetable toppings
The formula to find the total number of different sandwiches is:
\[ \text{Total Sandwiches} = (\text{Number of Bread Choices}) \times (\text{Number of Meat Choices}) \times (\text{Number of Cheese Choices}) \times (\text{Number of Vegetable Choices}) \]
Substitute the given numbers into the formula:
\[ \text{Total Sandwiches} = 3 \times 5 \times 5 \times 6 \]
Finally, compute the total:
\[ \text{Total Sandwiches} = 3 \times 5 \times 5 \times 6 = 450 \]
**Conclusion:**
You can order 450 different kinds of sandwiches at Underground.
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