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Use any method described in this section to solve each...

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Key Concepts

Combinations

Combinations focus on counting the number of ways to select a subset of items from a larger set when the order does not matter. The number of combinations is given by the formula n! divided by the product of r! and (n-r)! (often represented as C(n, r) or 'n choose r'), which represents the total number of distinct groups possible.

Permutations

Permutations involve counting the number of ways to arrange a subset of items from a larger set where the order of selection is important. The formula for calculating the number of permutations of choosing r items from n items is n! divided by (n-r)!, which provides the total number of ordered arrangements.

Fundamental Counting Principle

This principle states that if there are multiple independent choices or steps in a process, then the total number of outcomes is the product of the number of options available at each step. It is the underlying concept that allows the calculation of arrangements or selections in a systematic way.

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