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Combinations

from class:

Algebra and Trigonometry

Definition

Combinations are selections of items where the order does not matter. They are calculated using the binomial coefficient formula $\binom{n}{k} = \frac{n!}{k!(n-k)!}$.

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5 Must Know Facts For Your Next Test

  1. Combinations are used when the order of items does not matter, unlike permutations.
  2. The formula for combinations is $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ where $n$ is the total number of items and $k$ is the number of items to choose.
  3. Combinations can be related to Pascal's Triangle, where each entry represents a combination value.
  4. The concept of combinations is fundamental in probability theory for calculating possible outcomes.
  5. For large values of $n$ and $k$, combinations can be approximated using Stirling's approximation for factorials.

Review Questions

  • What is the difference between permutations and combinations?
  • How do you calculate the number of combinations when choosing 3 items from a set of 10?
  • Explain how Pascal's Triangle relates to combinations.
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