Problem 24 - College Algebra

Question

Evaluate each factorial expression. $$\frac{18 !}{16 !}$$

Step-by-Step Solution

Answer

The answer is \(306\).

Step 1: Understand Factorial Properties

Remember the property of factorials: n! = n*(n-1)!. You can use this property to simplify the factorial expression. In this expression, \(18!\) means the product of all positive integers from 18 to 1 and \(16!\) means the product of all positive integers from 16 to 1. So, \(16!\) is a part of \(18!\).

Step 2: Simplify the Expression

Rewrite \(18!\) as \(18 \times 17 \times 16!\). Hence the given expression can be written as \(\frac{18 \times 17 \times 16!}{16!}\). You can see that \(16!\) appears in both the numerator and the denominator, so they cancel out. Hence, the given expression simplifies to \(18 \times 17\).

Step 3: Evaluate the Result

Now, simply evaluate \(18 \times 17\) to find the final answer.