Evaluate C6 and 7P7. (If necessary, consult a list of formulas.) ₂% = C. 11 0 7³₁= 0
Evaluate C6 and 7P7. (If necessary, consult a list of formulas.) ₂% = C. 11 0 7³₁= 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate 9C6 and 7P7
![### Combinatorics and Permutations
Evaluate \( ^9C_6 \) and \( ^7P_7 \).
*(If necessary, consult a list of formulas.)*
\[ ^9C_6 = \boxed{} \]
\[ ^7P_7 = \boxed{} \]
### Explanation
This text is an exercise in combinatorics, asking to evaluate a combination and a permutation.
- **Combination (\( ^nC_r \))** is used when the order does not matter.
- **Permutation (\( ^nP_r \))** is used when the order does matter.
For these exercises, you may consider the following formulas:
- **Combination Formula:**
\[ ^nC_r = \frac{n!}{r!(n-r)!} \]
- **Permutation Formula:**
\[ ^nP_r = \frac{n!}{(n-r)!} \]
Where \( n! \) denotes the factorial of \( n \), which is the product of all positive integers up to \( n \).
Use these formulas to find the values of \( ^9C_6 \) and \( ^7P_7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36abf0e3-b64c-4a13-9d3d-62896715e253%2F841e1819-b074-4246-9796-197037a69df3%2Fmitjjif_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Combinatorics and Permutations
Evaluate \( ^9C_6 \) and \( ^7P_7 \).
*(If necessary, consult a list of formulas.)*
\[ ^9C_6 = \boxed{} \]
\[ ^7P_7 = \boxed{} \]
### Explanation
This text is an exercise in combinatorics, asking to evaluate a combination and a permutation.
- **Combination (\( ^nC_r \))** is used when the order does not matter.
- **Permutation (\( ^nP_r \))** is used when the order does matter.
For these exercises, you may consider the following formulas:
- **Combination Formula:**
\[ ^nC_r = \frac{n!}{r!(n-r)!} \]
- **Permutation Formula:**
\[ ^nP_r = \frac{n!}{(n-r)!} \]
Where \( n! \) denotes the factorial of \( n \), which is the product of all positive integers up to \( n \).
Use these formulas to find the values of \( ^9C_6 \) and \( ^7P_7 \).
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