Selecting a committee In how many ways can you select a committee of 3 Republicans and 3 Democra

step 1 We've got 18 Democrats and 11 Republicans, and we need to pick three people from each party for

Selecting a committee In how many ways can you select a...

Key Concepts

Combinations

Combinations are a counting principle used to determine the number of ways to select items from a larger set where the order of selection does not matter. They are typically expressed using the binomial coefficient, often denoted as C(n, r) or n choose r, which calculates the number of possible subsets of r elements from a set of n elements.

Binomial Coefficient

The binomial coefficient is a mathematical expression that represents the number of ways to choose a subset of a specific size from a larger set, without regard to the order of selection. It is calculated using the formula C(n, r) = n! / (r!(n - r)!), where n! denotes the factorial of n, summarizing the product of all positive integers up to n.

Multiplication Principle

The multiplication principle, also known as the rule of product, is a fundamental counting technique used when making a sequence of independent choices. When an event can be separated into inconsequential parts, the total number of outcomes is the product of the number of ways each individual part can occur.

Committee Selection

Committee selection is a type of combinatorial problem where a committee is formed by selecting certain members from larger groups. Such problems often involve applying combination formulas to different subgroups and then using the multiplication principle to combine the different selection processes.

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