Question - Factorial Expression Evaluation
Solution:
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 $$\frac{1}{8}$$.
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