Evaluate the expression. 8P2 O A. 336 Ов. 8 C. 56 O D. 1 O0 0 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Evaluate the Expression**
Given expression:
\[ ^8P_2 \]
Choices:
- A. 336
- B. 8
- C. 56
- D. 1
**Explanation:**
The expression \(^8P_2\) refers to the number of permutations of 8 items taken 2 at a time. The formula for permutations is:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
Substituting the values:
- \( n = 8 \)
- \( r = 2 \)
\[
^8P_2 = \frac{8!}{(8-2)!} = \frac{8!}{6!}
\]
This can be calculated as:
\[
8 \times 7 = 56
\]
Therefore, the correct answer is C. 56.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6cb1990-6e90-47a1-997c-36a24738006c%2Fcbb43cfa-d5c0-450a-915d-748ab309d603%2F1scitjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the Expression**
Given expression:
\[ ^8P_2 \]
Choices:
- A. 336
- B. 8
- C. 56
- D. 1
**Explanation:**
The expression \(^8P_2\) refers to the number of permutations of 8 items taken 2 at a time. The formula for permutations is:
\[
^nP_r = \frac{n!}{(n-r)!}
\]
Substituting the values:
- \( n = 8 \)
- \( r = 2 \)
\[
^8P_2 = \frac{8!}{(8-2)!} = \frac{8!}{6!}
\]
This can be calculated as:
\[
8 \times 7 = 56
\]
Therefore, the correct answer is C. 56.
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