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!

Composition problem help

  1. Oct 8, 2009 #1
    1. The problem statement, all variables and given/known data

    An astronaut crew is preparing for a space mission. As part of their preparation,
    they must spend a block of consecutive days training in a flight simulator. Each day,
    the crew is required to spend either 1, 2, or 3 hours in the simulator. The training
    ends once they attain n hours of simulator time.
    How many ways can the crew achieve the required n hours of training? Express your
    answer as a coefficient of a generating function.


    2. Relevant equations
    Generating functions. sum lemma. product lemma.


    3. The attempt at a solution

    Let Sk be the set Sk={1,2,3}^k
    and let S= U(union) Sk
    k>=0

    By the sum and product lemmas
    Is(x) (the generating function)= sigma Isk(x)
    k>= 0
    = sigma (I (x))^k
    k>=0 {1,2,3}
    = sigma (x+x^2+x^3)^k
    k>=0

    = 1/ (1- (x+x^2+x^3))

    therefore the number of ways the crew can achieve the required n hours of training is
    [x^n](coefficient)(1/(1-(x+x^2+x^3)).

    have i made any mistakes. am i completely off? any help would be greatly appreciated.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted