Question

evaluate.
\\(\frac{15!}{11!}\\)
the solution is \\(square\\).

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, \( 15! = 15\times14\times13\times12\times11! \).

Step2: Simplify the fraction

Substitute \( 15! \) in the given expression \( \frac{15!}{11!} \). We get \( \frac{15\times14\times13\times12\times11!}{11!} \). The \( 11! \) terms in the numerator and denominator cancel out.

Step3: Calculate the product

Now we calculate \( 15\times14\times13\times12 \).
First, \( 15\times14 = 210 \).
Then, \( 210\times13 = 2730 \).
Finally, \( 2730\times12 = 32760 \).

Answer:

\( 32760 \)