Arizona State University (ASU) ECN221 Business Statistics Exam 2 Practice

The correct answer for the formula for calculating combinations is represented by the first choice, which states that combinations can be calculated using the formula C(n, k) = n! / [k!(n - k)!]. This formula is fundamental in combinatorics and is used to determine the number of ways to choose k elements from a set of n elements without regard to the order of selection. The numerator, n!, represents the total arrangements of n elements. The denominator consists of k! and (n - k)!, where k! accounts for the arrangements of the selected elements and (n - k)! accounts for the arrangements of the elements that are not selected. By dividing the total arrangements by the arrangements of the selected and unselected elements, the formula effectively counts only the unique selections. Understanding this formula is crucial for solving various problems in statistics and probability, as it allows for the calculation of combinations in scenarios where the order of selection does not matter, such as in lottery combinations or in forming teams.