Binomial coefficient
from class: Algebra and Trigonometry Definition A binomial coefficient, denoted as $\binom{n}{k}$, represents the number of ways to choose $k$ elements from a set of $n$ elements without regard to order. It is an essential component in the expansion of binomial expressions.
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Predict what's on your test 5 Must Know Facts For Your Next Test The formula for calculating a binomial coefficient is $\binom{n}{k} = \frac{n!}{k!(n-k)!}$. Binomial coefficients are used in the Binomial Theorem to expand expressions of the form $(a+b)^n$. $\binom{n}{k}$ is equal to $\binom{n}{n-k}$ due to symmetry. Binomial coefficients can be found in Pascal's Triangle; each entry is the sum of the two directly above it. They are also used in combinatorial problems and probability calculations. Review Questions What is the binomial coefficient $\binom{5}{2}$ and how do you calculate it? Explain how binomial coefficients are related to Pascal's Triangle. How does the Binomial Theorem use binomial coefficients? "Binomial coefficient" also found in:
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