Question

1. simplify \\(\frac{7!}{5!}\\) = enter your next step here

Explanation:

Step1: Recall factorial definition

The factorial of a number \( n \), denoted as \( n! \), is defined as \( n! = n \times (n - 1) \times (n - 2) \times \dots \times 1 \). So, \( 7! = 7\times6\times5! \).

Step2: Substitute and simplify

Substitute \( 7! = 7\times6\times5! \) into the fraction \( \frac{7!}{5!} \), we get \( \frac{7\times6\times5!}{5!} \). The \( 5! \) terms in the numerator and denominator cancel out, leaving \( 7\times6 \).

Step3: Calculate the product

\( 7\times6 = 42 \).

Answer:

\( 42 \)