Final answer:
By using the fundamental counting principle, we calculate the total number of ways a student can answer a 7-question multiple-choice test with 5 options each to be 5 to the power of 7, resulting in 78,125 different combinations.
Step-by-step explanation:
If a student is taking a multiple-choice test with 7 questions, and each question has 5 choices, we can find the total number of ways the student can answer the questions by using the fundamental counting principle. This principle states that if there are n ways to do one thing, and m ways to do another, then there are n × m ways to do both.
For each question, there are 5 ways to choose an answer, and there are 7 independent questions. Applying the fundamental counting principle, we multiply the number of ways for each question:
- Question 1: 5 ways
- Question 2: 5 ways
- Question 3: 5 ways
- Question 4: 5 ways
- Question 5: 5 ways
- Question 6: 5 ways
- Question 7: 5 ways
Therefore, the total number of ways the student can answer the test is 5 ⁷, which is 78,125 different combinations.