Final answer:
The number of possible tutoring schedules with seven tutors, each working one hour per day, is determined by permutations. With no additional restrictions provided in the question, the answer would be 7 factorial (5040 possible schedules), which is not listed in the options, suggesting there may be an error in the question itself.
Step-by-step explanation:
The question is about computing the number of different tutoring schedules possible given certain conditions. There are seven tutors in total to be assigned to seven hours of work at a math center, which means one tutor per hour. Since there are three junior tutors and four senior tutors, we must consider how they can be arranged in a schedule, taking into account that the order in which they work matters. This is a problem of permutations.
To find the number of different schedules, we use the formula for permutations of a set, which is given by the factorial of the number of items. In this case, we have seven tutors and seven slots, so the number of different schedules is 7!, which equals 5,040. However, this is not one of the options provided, so let's check the conditions again to see if there are further restrictions.
Since the question does not give further conditions that restrict the ways the tutors can be scheduled, it's possible there might be an error in the question. Typically, with permutation problems, we would simply calculate the number of ways to arrange 7 different items, which in this case are the 7 tutors. Without additional conditions or restrictions, the number of different schedules is simply 7 factorial (7!).