(1) \( \frac{10!}{4!} \)

To solve \( \frac{10!}{4!} \), we first need to understand what factorials are. The notation \( n! \) (n factorial) means multiplying all whole numbers from \( n \) down to 1. Thus, \( 10! \) is \( 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \) and \( 4! \) is \( 4 \times 3 \times 2 \times 1 \). When we calculate \( \frac{10!}{4!} \), this simplifies beautifully because the \( 4! \) in the denominator cancels out the \( 4! \) portion of \( 10! \). So, you're left with \( 10 \times 9 \times 8 \times 7 \times 6 \times 5 \), which equals 50400. Voilà!