Evaluate the factorial expression. 22! 18!
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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![**Topic: Evaluating Factorial Expressions**
**Problem Statement:**
Evaluate the factorial expression.
\[
\frac{22!}{18!}
\]
**Solution Approach:**
To simplify the given expression \(\frac{22!}{18!}\), note that \(22! = 22 \times 21 \times 20 \times 19 \times 18!\). Therefore, the expression becomes:
\[
\frac{22 \times 21 \times 20 \times 19 \times 18!}{18!}
\]
By canceling out \(18!\) in the numerator and the denominator, the expression simplifies to:
\[
22 \times 21 \times 20 \times 19
\]
Evaluate this product to get the final answer.
**Exercise:**
Calculate \(22 \times 21 \times 20 \times 19\) to find the value of the expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F022ae44f-636d-4b99-a07b-5f1c14bbf99e%2F8eb331eb-e459-46f4-87cb-474e1c2ac70d%2Falvei0r_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Evaluating Factorial Expressions**
**Problem Statement:**
Evaluate the factorial expression.
\[
\frac{22!}{18!}
\]
**Solution Approach:**
To simplify the given expression \(\frac{22!}{18!}\), note that \(22! = 22 \times 21 \times 20 \times 19 \times 18!\). Therefore, the expression becomes:
\[
\frac{22 \times 21 \times 20 \times 19 \times 18!}{18!}
\]
By canceling out \(18!\) in the numerator and the denominator, the expression simplifies to:
\[
22 \times 21 \times 20 \times 19
\]
Evaluate this product to get the final answer.
**Exercise:**
Calculate \(22 \times 21 \times 20 \times 19\) to find the value of the expression.
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