Answer: a) 390,625, b) 2916.
Step-by-step explanation:
Since we have given that
Number of possible grades = 5
a) Number of students = 8
Using the "Fundamental theorem of counting", we get that
![5\times 5\times 5\times 5\times 5\times 5\times 5\times 5\\\\=5^8\\\\=390,625](https://tex.z-dn.net/?f=5%5Ctimes%205%5Ctimes%205%5Ctimes%205%5Ctimes%205%5Ctimes%205%5Ctimes%205%5Ctimes%205%5C%5C%5C%5C%3D5%5E8%5C%5C%5C%5C%3D390%2C625)
b) Number of students = 7
Number of students receive F = 0
Number of students receive A = 1
Number of remaining grades = 4
So, Using fundamental theorem of counting , we get that
![4\times 3\times 3\times 3\times 3\times 3\times 3\\\\=4\times 3^6\\\\=2916](https://tex.z-dn.net/?f=4%5Ctimes%203%5Ctimes%203%5Ctimes%203%5Ctimes%203%5Ctimes%203%5Ctimes%203%5C%5C%5C%5C%3D4%5Ctimes%203%5E6%5C%5C%5C%5C%3D2916)
Hence, a) 390,625, b) 2916.