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Chapter 8: Problem 23

Evaluate each factorial expression. $$\frac{17 !}{15 !}$$

Short Answer

Expert verified
The evaluated expression of \(\frac{17 !}{15 !}\) is 272

Step by step solution

01

Identify and Simplify

First, identify the factorials and consider that 17! is equal to \(17 脳 16 脳 15 脳 14 脳 ... 脳 1\) and 15! is \(15 脳 14 脳 ... 脳 1\). You'll notice that many values in 17! are also in 15!. This factor can be simplified.
02

Cancel Common Factors

Because the expression is a fraction, we can cancel out the common factors in the numerator (17!) and denominator (15!). When we do this, we're actually left with only \(17 脳 16\) in the numerator because all the other terms have been cancelled.
03

Calculate

Finally, calculate the value by multiplying the remaining factors. \(17 脳 16 = 272\).

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