In Exercises 9–16, use the formula for nCr to evaluate each expression. 5C0

Key Concepts

Combination

A combination is a selection of items from a larger set where the order of selection does not matter. In combinatorial mathematics, combinations are used to determine how many ways a certain number of items can be chosen from a larger group. The notation nCr represents the number of combinations of n items taken r at a time.

Binomial Coefficient

The binomial coefficient, denoted as nCr, is a mathematical expression that calculates the number of ways to choose r elements from a set of n elements without regard to the order of selection. It is calculated using the formula nCr = n! / (r!(n-r)!), where '!' denotes factorial, the product of all positive integers up to that number.

Factorial

A factorial, represented by n!, is the product of all positive integers from 1 to n. Factorials are fundamental in permutations and combinations, as they help calculate the total arrangements or selections of items. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120, and it is crucial for evaluating expressions involving nCr.