2. \( \frac{6!}{5!} \)

To solve \( \frac{6!}{5!} \), you simply divide the factorials. Since \( 6! = 6 \times 5! \), you can cancel \( 5! \) from the numerator and the denominator. This gives you \( 6 \). So, the expression simplifies to \( 6 \). Now, let's look at why factorials matter: they pop up everywhere, from counting permutations and combinations in probability to calculating coefficients in algebraic expansions! They're like the superheroes of mathematics, helping us unlock solutions in various fields. As a tip, a common mistake when working with factorials is not remembering that \( n! \) always includes all integers down to 1. Also, keep in mind that \( 0! \) is defined as \( 1 \). Whenever you're unsure, just remember that factorials are all about multiplying down, and you'll do just fine!