Number of Possible Arrangements (Permutations?)

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Homework Help Overview

The discussion revolves around a multiple-choice test consisting of 5 questions, each with 4 possible answers. Participants are exploring how to calculate the number of ways a student can select answers, both for all questions and specifically for getting all answers wrong.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the multiplication rule for determining the number of arrangements of answers. There is also a question about whether permutations are relevant to the problem. The original poster seeks hints to clarify their approach.

Discussion Status

Some participants have provided insights into the calculations for part (a) and part (b), suggesting the use of the multiplication rule. There is an ongoing exploration of the reasoning behind the choices for each question and how to apply these to the overall problem.

Contextual Notes

Participants are navigating the rules of combinations and permutations in the context of a homework assignment, with an emphasis on understanding the underlying principles rather than arriving at a final answer.

Saladsamurai
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Homework Statement


If a multiple-choice test consists of 5 questions each with 4 possible answers of which only 1 is correct,

(a) In how many different ways can a student check off one answer to each question?

(b) In how many different ways can a student check off one answer to each question and get all the answers wrong?


I feel like if I could get a hint on (a) I could do (b) as well, but I am a little stuck trying to figure out which rule to apply. These are permutations correct? (the arrangement of answers.)

Or should I just apply the "multiplication rule" somehow?
Can I get just a hint here?
 
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a) How many ways are there to answer ONE question? i.e. How many ways are there to PICK/CHOOSE one of the four answers? How many ways are there to do this for 5 questions?
 
The Chaz said:
a) How many ways are there to answer ONE question? i.e. How many ways are there to PICK/CHOOSE one of the four answers? How many ways are there to do this for 5 questions?

Let's denote each answer choice for each question as a, b, c, d.

So for each question there are 4 different ways to answer. Oh. So it is 4^5 = 1024. So it is the multiplication rule.
 
So I suppose for part (b) since I have (4-1) choices for each, the answer would be (4-1)^5 = 243.
 
Sounds good to me!
 
Thanks homes!
 

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