B. Evaluate each. 1. C(8,4) 22. C(5,0) 3. C(4,4) 4. C(11,3) C(7,4) 5. C(8,4) C(7,5)mm MDH inch ball 6. C(8,2) C(6,2) C(4,2) beggibyen 8 ensindo Puno a to od A eodores rosa team of ostopise o curso nahsyns begoib yaoud in to

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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).
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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