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

Evaluate
6151
8121
Simplify your answer as much as possible.
Transcript text: Evaluate 6151 8121 Simplify your answer as much as possible.
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Solution

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Solution Steps

Step 1: Expand the factorials

First, expand \(6!\) and \(5!\): \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]

Step 2: Substitute the expanded factorials into the expression

Substitute the expanded forms of \(6!\) and \(5!\) into the expression \(\frac{6!}{5!}\): \[ \frac{6!}{5!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \]

Step 3: Simplify the expression

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

\(\boxed{6}\)

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