1. Not finding help here? Sign up for a free 30min 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!

Math counting problem

  1. May 25, 2007 #1


    User Avatar
    Gold Member

    To open a safe, 4 number buttons must be pressed, in the correct order. Over time, the 4 numbers buttons of the code fade. A thief notices the faded buttons, so knows that the code consists of those 4 numbers.

    How many possible codes are there?

    4 numbers can be arranged in 4! different ways, so there are 24 different possible combinations.

    The safe owner decides that he wants to change the code. How many possible codes are possible if each code can contain only 1 of the 4 faded numbers?

    ^4 C_1 \times ^8 C_3 \times 4!=5376

    Since there are two groups, faded and non faded. One is selected from the faded numbers, and 3 from the remaining 8 non faded. i then multiplied by 4! since there are 4! ways of arranging the 4 numbers.

    The answer guide says this is wrong though. Is anybody able to explain where i went wrong in my reasoning?

  2. jcsd
  3. May 25, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    At first glance I would say that it has to do with the fact that you think 8 are non-faded. If there is a button for each digit then there will 10 buttons, 4 of which have faded. Thus there will be 6 non-faded buttons.
  4. May 25, 2007 #3


    User Avatar
    Gold Member

    The buttons arent 0-9, theyre 1-12. There was a diagram with the question that showed this.
  5. May 25, 2007 #4


    User Avatar
    Science Advisor
    Homework Helper

    No repeated numbers allowed, right? And "can contain only 1 of the 4" means "contains exactly one of the 4"? If those are both correct then I can't see anything wrong with your solution.
  6. May 25, 2007 #5


    User Avatar
    Gold Member

    Yep thats right. No repeats allowed, and EXACTLY 1 of the 4.

    Well thanks for clearing that up. Glad i did it correctly then.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Math counting problem
  1. Counting problem. (Replies: 8)

  2. Counting problem (Replies: 3)

  3. Counting problem (Replies: 3)

  4. Counting math problem (Replies: 6)