Math 2602  A1 - A3                                                                             Homework  #6
                                             Due Thursday, October 6, 2005


       1.  i)  Find the number of ways to distribute 20 distinct objects to 5 distinct locations so that exactly
                three objects are sent to the first location.

            ii) Find the number of ways to distribute 20 distinct objects to 4 distinct locations so that at least
                one object is sent to the first location.

          (NOTE:  Think of "words" whose  entries answer the questions: Where does the first object  go?,
            Where does the second object go?, Where does the third object go? etc.  How long would these
             words need to be?  How large an alphabet would you need?)


     2.   a) Find the generating function for the number of ways to distribute indistinguishable objects to 3
            (distinguishable ) locations so that

           i) the first location receives at least 2 objects.

           ii) each location receives at most 4 objects.

         b)  Find the coefficient of  x²⁰ (which gives the number of ways to distribute 20 objects) in each
             of the generating functions in (a).