Number of Possible Arrangements (Permutations?)

[Saladsamurai]

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?

 

[The Chaz]

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?

 

[Saladsamurai]

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.

 

[Saladsamurai]

So I suppose for part (b) since I have (4-1) choices for each, the answer would be (4-1)^5 = 243.

 

[The Chaz]

Sounds good to me!

 

[Saladsamurai]

Thanks homes!