First, expand \(6!\) and \(5!\): \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]
Substitute the expanded forms of \(6!\) and \(5!\) into the expression \(\frac{6!}{5!}\): \[ \frac{6!}{5!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \]
Cancel out the common terms in the numerator and denominator: \[ \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} = 6 \]
The simplified result is \(6\).
\(\boxed{6}\)
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