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Chapter 11: Problem 14

Evaluate each factorial expression. \(\frac{12 !}{10 !}\)

Short Answer

Expert verified
The result of the expression \(\frac{12 !}{10 !}\) is 132.

Step by step solution

01

Understand Factorial Operation

The factorial of a positive integer n, denoted by \(n!\), is the product of all positive integers less than or equal to n. In the given expression \(\frac{12 !}{10 !}\), both 12 and 10 have their own factorials.
02

Apply the Property of Factorial Operation

The property of the factorial operation allows to simplify \(\frac{12 !}{10 !}\) into \(12 * 11\). This property holds because \(12!\) is equal to \(12 * 11 * 10!\) and \(10!\) is equal to \(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1\). You can see that we can cancel out \(10!\) in the numerator and denominator.
03

Compute the Result

Once the expression is simplified, just multiply the numbers: \(12 * 11 = 132\).

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