Problem 23
Question
Evaluate each factorial expression. $$\frac{17 !}{15 !}$$
Step-by-Step Solution
Verified Answer
The evaluated expression of \(\frac{17 !}{15 !}\) is 272
1Step 1: Identify and Simplify
First, identify the factorials and consider that 17! is equal to \(17 × 16 × 15 × 14 × ... × 1\) and 15! is \(15 × 14 × ... × 1\). You'll notice that many values in 17! are also in 15!. This factor can be simplified.
2Step 2: 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 \(17 × 16\) in the numerator because all the other terms have been cancelled.
3Step 3: Calculate
Finally, calculate the value by multiplying the remaining factors. \(17 × 16 = 272\).
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