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!

Fundamental Counting Principle problem

  1. Dec 15, 2003 #1
    The dial on a 3 number combination lock contains markings to represent the numbers from 0 to 59. How many combinations are possible if the first and second numbers differ by 3?

    What I did was:

    1st number: It can be any of the 60 numbers (if we take 0 also as a #)
    2nd number: I think since there are two possibilities, either 3 greater than 1st # or 3 less
    3rd number: Since you've already take a number for the first one, and you must choose either of 3 less or 3 greater than the first number as the 2nd #, you must in the end have 57 #'s left to choose from

    Therefore the answer I think is 60 x 2 x 57

    Is that right?
     
  2. jcsd
  3. Dec 15, 2003 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Not quite. If the first number is 57, 58 or 59, then the next number CAN'T be "3 larger" but only 3 less. If the first number is 0, 1, or 2, the next number CAN'T be "3 less but only 3 more.
    That is, if the first number is 3 to 56 (54 numbers) then there are 2 possible second number but if the first number is 0, 1, 2, 57, 58, or 59, then there is only 1 possible second number. There are 54*2+ 3+ 3= 114 possible two digit combinations for the first two numbers. There are 114*60= 6840 such three digit combinations.
     
  4. Dec 15, 2003 #3

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Halls,

    While he didn't explicity state it, I would think that you can go "over the top" and consider 59 and 2 to differ by 3.

    Pi,

    I think you're almost correct. However, if you choose one of 60 numbers, then choose one of the 59 remaining, there are 58 left -- NOT 57.

    - Warren
     
  5. Dec 15, 2003 #4
    Thanks for the replies guys. Hall I dont understand why you did 54*2 and added 6
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fundamental Counting Principle problem
  1. A counting problem (Replies: 2)

  2. Counting Problem (Replies: 3)

Loading...