Factorial Expression Evaluation
The image shows a mathematical problem that asks to evaluate the expression:
\[ \frac{7!}{8!} \]
Here "!" represents the factorial operation, which means the product of all positive integers up to that number. For example, \(7!\) is \(7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).
Now let's evaluate the expression by writing out the factorials:
\[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]
\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]
Substituting these into the original equation:
\[ \frac{7!}{8!} = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \]
In this fraction, every term in \(7!\) cancels out with its corresponding term in \(8!\), except for the 8 in the denominator:
\[ \frac{7!}{8!} = \frac{1}{8} \]
So the evaluated expression is \(\frac{1}{8}\).
