Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Answer numbers 4 to 6
![Certainly! The provided image seems to contain a list of combination (binomial coefficient) problems under a section titled "B. Evaluate each".
Here is the transcribed text from the image:
---
**B. Evaluate each.**
1. C(8,4)
2. C(5,0)
3. C(4,4)
4. C(11,3) • C(7,4)
5. C(8,4) • C(7,5)
6. C(8,2) • C(6,2) • C(4,2)
---
These are mathematical problems involving binomial coefficients, commonly read as "n choose k", which represent the number of ways to choose k items from n items without regard to the order of selection.
For example:
- **C(8,4)** represents the number of combinations to choose 4 items from 8.
- **C(5,0)** represents the number of ways to choose 0 items from 5 (which is always 1 by definition).
- **C(4,4)** represents the number of ways to choose 4 items from 4 (also 1 by definition).
In the cases where combinations are multiplied:
- **C(11,3) • C(7,4)** represents the product of the number of ways to choose 3 items from 11, and the number of ways to choose 4 items from 7.
- **C(8,4) • C(7,5)** is the product of combinations choosing 4 out of 8 and 5 out of 7 respectively.
- **C(8,2) • C(6,2) • C(4,2)** is the product of combinations choosing 2 out of 8, 2 out of 6, and 2 out of 4 respectively.
Remember, the binomial coefficient is calculated using the formula:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Where \( n \) is the total number of items, \( k \) is the number of items to choose, and \( ! \) denotes factorial (the product of all positive integers up to that number).](https://content.bartleby.com/qna-images/question/f534fa3a-7fc6-4517-a79f-1e1d7853b104/c7ed2d9c-65ad-45a6-b3e3-09255fd6ce0d/f65i8z_processed.jpeg)
Transcribed Image Text:Certainly! The provided image seems to contain a list of combination (binomial coefficient) problems under a section titled "B. Evaluate each".
Here is the transcribed text from the image:
---
**B. Evaluate each.**
1. C(8,4)
2. C(5,0)
3. C(4,4)
4. C(11,3) • C(7,4)
5. C(8,4) • C(7,5)
6. C(8,2) • C(6,2) • C(4,2)
---
These are mathematical problems involving binomial coefficients, commonly read as "n choose k", which represent the number of ways to choose k items from n items without regard to the order of selection.
For example:
- **C(8,4)** represents the number of combinations to choose 4 items from 8.
- **C(5,0)** represents the number of ways to choose 0 items from 5 (which is always 1 by definition).
- **C(4,4)** represents the number of ways to choose 4 items from 4 (also 1 by definition).
In the cases where combinations are multiplied:
- **C(11,3) • C(7,4)** represents the product of the number of ways to choose 3 items from 11, and the number of ways to choose 4 items from 7.
- **C(8,4) • C(7,5)** is the product of combinations choosing 4 out of 8 and 5 out of 7 respectively.
- **C(8,2) • C(6,2) • C(4,2)** is the product of combinations choosing 2 out of 8, 2 out of 6, and 2 out of 4 respectively.
Remember, the binomial coefficient is calculated using the formula:
\[ C(n, k) = \frac{n!}{k!(n-k)!} \]
Where \( n \) is the total number of items, \( k \) is the number of items to choose, and \( ! \) denotes factorial (the product of all positive integers up to that number).
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