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
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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 \( ^7P_7 \).
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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