Possible grades for a class are A B C D and F no s A how man

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 seven students?

B) how many ways are there to assign grades to a class of seven students if noday receives an F and exactly one person receives an A?

Solution

Possible grades include A, B, C, D, and F.
1. Seven students in a class, how many ways can a teacher assign grades to the class
Each of the seven can get either of the 5 grades
Ans: 5*7 = 78125 ways

Ways to give the A = 7
Ways to grade the remaining 6 students: 4^6 = 4096
Ans: 7*4096 = 28672