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Chapter 11: Problem 18

Evaluate each factorial expression. \(\frac{17 !}{9 !}\)

Short Answer

Expert verified
The value of \( \frac{17!}{9!} \) equals to the product of all integers from 17 to 10 inclusive, which is 17643225600.

Step by step solution

01

Understand the Factorial Notation

The factorial operation is defined as the product of all positive integers less than or equal to the number. It is denoted by the symbol '!'. For instance, for a number \( n \), \( n! = n \times (n-1) \times (n-2) \times \ldots \times 2 \times 1 \). Therefore, \( 17! = 17 \times 16 \times 15 \times \ldots \times 2 \times 1 \) and \( 9! = 9 \times 8 \times 7 \times \ldots \times 2 \times 1 \).
02

Write Out the Factorials

To compute \( \frac{17!}{9!} \), one should express both 17! and 9! as factor of descending order. So, we get: \( \frac{17!}{9!} = \frac{17 \times 16 \times 15 \times 14 \times \ldots \times 2 \times 1}{9 \times 8 \times 7 \times \ldots \times 2 \times 1} \).
03

Simplify the Factorial division

Notice that all the numbers in the denominator exist in the numerator. So they can cancel out each other leaving us with the factorial multiplication from 17 down to 10. So we get: \( 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \)
04

Compute the Product

Finally, compute this product to obtain the result.

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