Problem 24 - College Algebra

Question

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

Step-by-Step Solution

Answer

The evaluation of the expression \(\frac{18 !}{16 !}\) is 306.

Step 1: Expanding the Factorials

Expand the larger factorial in the expression, but only down to the smaller factorial. The expression becomes \(\frac{18*17*16!}{16!}\).

Step 2: Cancelling Common Terms

Cancel out the common terms in the numerator and the denominator. In this case, \(16!\) is common to both the numerator and the denominator, so after cancellation, the expression simplifies to \(18*17\).

Step 3: Multiply the Remaining Terms

Multiply the remaining terms in the numerator to get the final result. \(18*17 = 306\).