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?
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?
Please select the School Subject carefully. 8th grade will not get the proper teacher to read and answer your post.
Sra
Maybe you should just make it as math instead of 8th grade. I suggest you post it agin.
To find the total number of combinations, we can use the concept of combinations and the binomial coefficient.
For the first scenario where we know Michael has earned at least one of each of the 5 letter grades, we need to determine the combinations for the remaining 2 grades. Since order is not important, we can calculate the combinations using the formula:
C(n, r) = n! / (r!(n-r)!)
Where:
n = total number of options (5 letter grades + 2 remaining grades)
r = number of choices (2 remaining grades)
Plugging in the values:
C(7, 2) = 7! / (2!(7-2)!)
= 7! / (2!(5)!)
= (7 * 6 * 5!)/(2 * 5!)
= (7 * 6)/(2)
= 21
Therefore, for the first scenario, there are a total of 21 combinations of 7 final grades that Michael can receive for the first grading period.
Now, for the second scenario where we do not know any of Michael's 7 final grades, we will again calculate the combinations for all 7 grades. Using the formula:
C(n, r) = n! / (r!(n-r)!)
Plugging in the values:
C(5 + 7 - 1, 7) = C(11, 7)
= 11! / (7!(11-7)!)
= (11 * 10 * 9 * 8 * 7!)/(7! * 4!)
= 330
Therefore, in the second scenario, there are a total of 330 combinations of 7 final grades that Michael can receive for the first grading period, considering we do not know any of the grades in advance.