Question

Possible grades for a class are A, B, C, D, and F. (No +/− 's.)

(a) How many ways are there to assign grades to a class of eight students?


(b) How many ways are there to assign grades to a class of seven students if nobody receives an F and exactly one person receives an A?

Answer 1

Answer: a) 390,625, b) 2916.

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* 5* 5* 5* 5* 5* 5* 5\\\\=5^8\\\\=390,625`

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* 3* 3* 3* 3* 3* 3\\\\=4* 3^6\\\\=2916`

Hence, a) 390,625, b) 2916.