Question

evaluate \\(\frac{18!}{12!}\\). enter your answer in the box.

Explanation:

Step1: Recall factorial definition

The factorial of a number \( n \), denoted as \( n! \), is the product of all positive integers from \( 1 \) to \( n \). So, \( 18! = 18\times17\times16\times15\times14\times13\times12! \).

Step2: Simplify the fraction

Substitute \( 18! \) in the given expression \( \frac{18!}{12!} \). We get \( \frac{18\times17\times16\times15\times14\times13\times12!}{12!} \). The \( 12! \) terms cancel out, leaving \( 18\times17\times16\times15\times14\times13 \).

Step3: Calculate the product

First, \( 18\times17 = 306 \), \( 306\times16 = 4896 \), \( 4896\times15 = 73440 \), \( 73440\times14 = 1028160 \), \( 1028160\times13 = 13365960 \).

Answer:

\( 13365960 \)