1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Number of Possible Arrangements (Permutations?)

  1. May 18, 2010 #1
    1. The problem statement, all variables and given/known data
    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?
  2. jcsd
  3. May 18, 2010 #2
    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?
  4. May 18, 2010 #3
    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.
  5. May 18, 2010 #4
    So I suppose for part (b) since I have (4-1) choices for each, the answer would be (4-1)^5 = 243.
  6. May 18, 2010 #5
    Sounds good to me!
  7. May 19, 2010 #6
    Thanks homes!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook