On the last school day of the first grading period Michael learns his final grade for each class. If order is not important and we know he has earned at least 1 of each of the 5 letter grades, what is the total number of combinations of 7 final grades (one for each class) that Michael can possibly receive for the first grading period?
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Assume now that we do not know any of Michael's 7 final grades. If order is not important, what is the total number of combinations of 7 final grades (one for each class) that Michael can possibly receive for the first grading period?
To find the total number of combinations of 7 final grades that Michael can possibly receive, we need to consider the number of options for each class grade and then multiply them together.
In the first scenario where we know he has earned at least 1 of each of the 5 letter grades, we still have 5 options for the grade in each class. The total number of combinations will be 5 raised to the power of 7, since we have 7 classes.
Therefore, the total number of combinations for the first grading period is 5^7 = 78,125.
In the second scenario where we don't know any of Michael's 7 final grades, we still have 5 options for each class. So the total number of combinations remains the same, 5^7 = 78,125.