Evaluate the factorial expression. 11! (11-3)! 11! (11-3)!
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 the Factorial Expression**
To evaluate the given factorial expression, follow the steps below:
\[ \frac{11!}{(11 - 3)!} \]
First, simplify the expression inside the factorial in the denominator:
\[ 11 - 3 = 8 \]
So, the expression becomes:
\[ \frac{11!}{8!} \]
Next, express \(11!\) as:
\[ 11! = 11 \times 10 \times 9 \times 8! \]
Substitute into the fraction:
\[ \frac{11 \times 10 \times 9 \times 8!}{8!} \]
Cancel out \(8!\) from the numerator and the denominator:
\[ 11 \times 10 \times 9 \]
Now, calculate the remaining multiplication:
\[ 11 \times 10 = 110 \]
\[ 110 \times 9 = 990 \]
Thus, the value of the expression is:
\[ \frac{11!}{(11 - 3)!} = 990 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F022ae44f-636d-4b99-a07b-5f1c14bbf99e%2F2d72032b-1e2d-4bb4-9b81-c36a05561b21%2F852akpc_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the Factorial Expression**
To evaluate the given factorial expression, follow the steps below:
\[ \frac{11!}{(11 - 3)!} \]
First, simplify the expression inside the factorial in the denominator:
\[ 11 - 3 = 8 \]
So, the expression becomes:
\[ \frac{11!}{8!} \]
Next, express \(11!\) as:
\[ 11! = 11 \times 10 \times 9 \times 8! \]
Substitute into the fraction:
\[ \frac{11 \times 10 \times 9 \times 8!}{8!} \]
Cancel out \(8!\) from the numerator and the denominator:
\[ 11 \times 10 \times 9 \]
Now, calculate the remaining multiplication:
\[ 11 \times 10 = 110 \]
\[ 110 \times 9 = 990 \]
Thus, the value of the expression is:
\[ \frac{11!}{(11 - 3)!} = 990 \]
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