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Binomial Coefficients and Combinatorics

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Multiple Choice

What is the formula for calculating the binomial coefficient of n and k, denoted as (\binom{n}{k})?

  1. $\(\binom{n}{k} = \frac{n!}{k!}\)
  2. $\(\binom{n}{k} = \frac{n!}{(n-k)!}\)
  3. $\(\binom{n}{k} = \frac{(n+k)!}{n!}\)
  4. $\(\binom{n}{k} = \frac{(n+k)!}{k!}\)
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