Questions: Evaluate 6151 8121 Simplify your answer as much as possible.

Solution Steps

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 \(6\).

Final Answer