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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?

Respuesta :

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

[tex]5\times 5\times 5\times 5\times 5\times 5\times 5\times 5\\\\=5^8\\\\=390,625[/tex]

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

[tex]4\times 3\times 3\times 3\times 3\times 3\times 3\\\\=4\times 3^6\\\\=2916[/tex]

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

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