Question 277121: I'm having difficulty with these problems if anyone could help I'd really appreciate it.
The first one:
A exam has 5 questions with 4 choices each and one correct answer per question
1. How many ways can you fill out a answer sheet
2. How many ways can you fill out the sheet to have 4 answers correct and 1 incorrect
3. If a student guesses randomly at each, what is the probability the student gets three or fewer correct
The second question:
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
2. How many ways can a teacher assign grades to seven students if nobody gets an F but only one student gets an A
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A exam has 5 questions with 4 choices each and one correct answer per question
1. How many ways can you fill out a answer sheet
# of ways to pick a question: 5
# of ways to answer a question: 4
Ans: 4*4*4*4*4 = 4^5 = 1024
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2. How many ways can you fill out the sheet to have 4 answers correct and 1 incorrect
# of ways to choose 1 incorrect answer: 5
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3. If a student guesses randomly at each, what is the probability the student gets three or fewer correct
Binomial Problem with n=5, p = 1/4 , 0<= x <=3
Using TI-84 I get binomcdf(5,1/4,3) = 0.9844
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The second question:
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
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2. How many ways can a teacher assign grades to seven students if nobody gets
an F but only one student gets an A
Ways to give the A = 7
Ways to grade the remaining 6 students: 4^6 = 4096
Ans: 7*4096 = 28672
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Cheers,
Stan H.
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