Final answer:
To find the number of ways four students can line up, we calculate 4 factorial (4!), which amounts to 24 different combinations.
Step-by-step explanation:
The task of determining the number of different ways four students - Daniel, Avani, Sydney, and Samantha - can stand in line is a combinatorics problem. The method used to solve this problem involves calculating permutations.
To find the number of ways to arrange four students in line, we calculate the factorial of the number of students, which in this case is 4! (four factorial). A factorial is the product of all positive integers up to a given number, so 4! = 4 × 3 × 2 × 1 = 24. Therefore, there are 24 different combinations or ways in which the four students can line up.
The step-by-step explanation involves understanding that for the first position in line, there are 4 possible choices. Once the first student is placed, there are 3 remaining students to choose from for the second position, 2 for the third position, and the last student will automatically take the fourth position.