Math 2602 B1 , B2                                                                                Homework #5        
        
                                             Due Thursday, September 25, 2003


  i)  Find the number of ways to select 16 objects with repetition from a set of 5 distinct objects
       (if the order in which they are selected is not considered).

      Note:  This is the number of non-negative integer solutions to  x₁ + x₂ +x₃ + x₄ + x₅ = 16 ,
      where x_i is the number of times object i is selected.

  ii)  In how many of the outcomes counted in (i) is the first object selected exactly 3 times?


  iii) In how many of the outcomes counted in (i) is the first object selected at least 3 times?


  iv) In how many of the outcomes counted in (i) is the first object selected at most 3 times?


  v)  In how many of the outcomes counted in (i) are each of the first two objects selected at
       least twice?


  vi) In how many of the outcomes counted in (i) are each of the first two objects selected at
       most twice?