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!

Function counting question

  1. Apr 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Let A = {1,2,3} and B = {1,2,3,4,5}
    Find the number of functions f: A -> B so that f(1) = f(2)


    2. Relevant equations



    3. The attempt at a solution

    I'm just reviewing random questions for my final on Tuesday and I came upon this question. Seems to be a counting question, and I'm not that sure how to do this since counting questions are more intuition than method (at least that's what I think). Here's what I got:

    So a function sends an element from 1 set to another.

    There are 3 possible values for the f function, namely f(1), f(2), and f(3).

    There are 75 possibilities (5*5*5). So I guess you have to pick the possible values of f(1), f(2) and f(3). So f(1) has 5 choices, f(2) has 1 choice because it must match what f(1) was mapped to, f(3) can be whatever, so it's 5 again.

    5 * 1 * 5 = 25

    So there are 25 possible functions.

    Is this correct? I always hated counting problems ><
     
  2. jcsd
  3. Apr 25, 2010 #2
    Yes, this is right, except that 5*5*5 = 125, not 75.

    This then leads to the intuitive result that 1/5 (25/125) of possible functions have f(1) = f(2).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Function counting question
  1. Counting question (Replies: 3)

  2. Counting question (Replies: 1)

Loading...