Final answer:
To calculate the number of ways the student can have fewer hours on Friday than on Thursday, we can use the concept of combinations. By following the steps outlined in the answer, the total number of ways can be calculated.
Step-by-step explanation:
To calculate the number of ways the student can have fewer hours on Friday than on Thursday, we can use the concept of combinations. Since the student has to take 8 hours of classes a week from Monday to Friday, one possible scenario is that they take 3 hours on Monday, 2 hours on Tuesday, 2 hours on Wednesday, 1 hour on Thursday, and 0 hours on Friday. This is one combination. We can also rearrange the hours in different ways, such as taking 2 hours on Monday, 3 hours on Tuesday, 2 hours on Wednesday, 1 hour on Thursday, and 0 hours on Friday. By considering all possible combinations, we can determine the total number of ways.
Using the concept of combinations, we can calculate the number of ways. Let's break it down:
- Choose the number of hours for Thursday: There are 8 hours in total, so we need to choose a number between 0 and 8. Let's assume we choose 1 hour for Thursday.
- Choose the number of hours for Friday: Since we want to have fewer hours on Friday than on Thursday, the number of hours for Friday can be chosen from the remaining 7 hours (8 - 1 = 7).
- Calculate the number of combinations: We can calculate the number of combinations using the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of hours (8), and r is the number of hours for Thursday. For our example, it would be 7C1 = 7! / (1!(7-1)!)
- Calculate the total number of combinations: Since we want to consider all possible values for Thursday, we need to sum up the number of combinations for each value of r (number of hours for Thursday). We can do this for r = 0, 1, 2, ..., 7.
By following these steps, we can calculate the total number of ways the student can have fewer hours on Friday than on Thursday.