Combinations
Definition
Combinations refer to the selection of items from a larger set where order does not matter. They are used to determine how many ways a subset of items can be chosen from the entire set without regard to the sequence of selection.
5 Must Know Facts For Your Next Test
- The formula for combinations is C(n, k) = n! / [k!(n - k)!], where n is the total number of items and k is the number of items to choose.
- Combinations are different from permutations because permutations consider order while combinations do not.
- In combinations, C(n, k) is equal to C(n, n - k), meaning choosing k items from n is the same as choosing (n - k) items from n.
- A combination problem often uses phrases like 'selecting', 'choosing', or 'picking' without concern for order.
- Binomial coefficients, often found in binomial expansions, are calculated using combinations.
Review Questions
- What distinguishes a combination from a permutation?
- How would you calculate the number of ways to choose 3 items out of a set of 7?
- Explain why C(10, 2) equals C(10, 8).
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Related terms
Permutation: An arrangement or listing where order matters.
Factorial: The product of all positive integers up to a given number; denoted by n!.
Binomial Coefficient: A component in binomial expansion that represents combinations and is written as (n choose k).
