Final Answer:
There are 24 possible ways for the teacher to assign 4 different tasks to her 4 students.
Step-by-step explanation:
To determine the number of ways the teacher can assign tasks to her students, we can use the fundamental counting principle. For the first task, she has 4 choices of students to assign it to. Once the first task is assigned, she has 3 students left to choose from for the second task, then 2 for the third task, and the last student receives the remaining task. The total number of ways to assign tasks is found by multiplying the number of choices at each step: 4 * 3 * 2 * 1 = 24.
This is because at each step, the number of available choices decreases by 1. The fundamental counting principle allows us to multiply the number of choices at each step to find the total number of outcomes. In this case, it results in 4 factorial (4!), which is the product of all positive integers up to 4. Therefore, the teacher can assign the tasks in 24 different ways.
In summary, the answer is obtained by realizing that for each task, there is a decreasing number of students to choose from, leading to 24 possible ways to assign 4 tasks to 4 students.