Combinations

Definition

A combination is a selection of items from a larger pool where the order does not matter. It is calculated using the binomial coefficient formula.

5 Must Know Facts For Your Next Test

1. The formula for combinations is given by $$C(n, r) = \frac{n!}{r!(n-r)!}$$.
2. Combinations differ from permutations in that order does not matter in combinations.
3. The symbol $$\binom{n}{r}$$ represents the number of ways to choose r items from n items without regard to order.
4. Combinations are used in binomial expansions, represented in the Binomial Theorem as coefficients.
5. In probability and counting problems, combinations help determine possible groupings or selections.

Review Questions

• What is the difference between a combination and a permutation?
• How do you calculate the number of combinations of choosing 3 items from a set of 7?
• $$\binom{5}{2}$$ equals what value?

Related terms

Permutation:

An arrangement of objects where order matters. Calculated using $$P(n, r) = \frac{n!}{(n-r)!}$$.

Binomial Coefficient:

A coefficient that gives the number of ways to choose k items from n without regard to order, denoted as $$\binom{n}{k}$$.

Factorial:

The product of all positive integers up to a given number n, denoted as $$n!$$.