Results 1 to 4 of 4

Math Help - exponential generating function

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    19

    exponential generating function

    Find the exponential generating function for a_n, the number of different arrangements of n objects chosen from 5 different types of objects with each object appearing
    a) at least 3 times
    b) no more than 7 times
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by sw2010 View Post
    Find the exponential generating function for a_n, the number of different arrangements of n objects chosen from 5 different types of objects with each object appearing
    a) at least 3 times
    b) no more than 7 times
    Hint for a):

    Suppose you just have only 1 type of object. Then no matter how many of the objects you have, there is only 1 way to arrange them. What is the EGF of the number of ways to arrange the objects if each object appears at least 3 times? Call this EGF f. Then the answer to a) is just f^5.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2010
    Posts
    19
    so would the answer to (b) be f^(7-n)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by sw2010 View Post
    so would the answer to (b) be f^(7-n)
    No, you need a new "f"-- this time the EGF for the number of ways to arrange the objects if each object appears no more than 7 times.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another exponential generating function
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: July 27th 2010, 07:35 PM
  2. Confused on Exponential Generating function
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: July 27th 2010, 10:25 AM
  3. Replies: 0
    Last Post: April 13th 2010, 09:37 PM
  4. Exponential Generating Function
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 3rd 2010, 10:30 AM
  5. moment generating function of exponential dist.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 24th 2008, 07:43 PM

Search Tags


/mathhelpforum @mathhelpforum