Question

find the exact value of the following expression.
\\(\binom{8}{1}\\)

Explanation:

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<reasoning>

State the binomial coefficient formula

\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]

Substitute the given values

\[

$$\begin{aligned} n &= 8 \\ k &= 1 \end{aligned}$$

\]

Calculate the exact value

\[
\binom{8}{1} = \frac{8!}{1!(8-1)!} = \frac{8!}{1! \cdot 7!} = 8
\]
</reasoning>

<answer>
8
</answer>

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"Mathematics",
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"Binomial Coefficient"
]
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</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
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],
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],
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</pre_analysis>

<reasoning>

State the binomial coefficient formula

\[
\binom{n}{k} = \frac{n!}{k!(n-k)!}
\]

Substitute the given values

\[

$$\begin{aligned} n &= 8 \\ k &= 1 \end{aligned}$$

\]

Calculate the exact value

\[
\binom{8}{1} = \frac{8!}{1!(8-1)!} = \frac{8!}{1! \cdot 7!} = 8
\]
</reasoning>

<answer>
8
</answer>

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"Mathematics",
"Algebra",
"Binomial Coefficient"
]
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