Math 2602  B1 , B2                                                                                Homework  #5
                                             Due Thursday, September 23, 2004


      i)   Find the number of ways to distribute 20 indistinguishable objects to 5 (distinguishable) locations
             (if the order in which they are distributed is not considered).

             Note:  This is the number of non-negative integer solutions to  x₁ + x₂ + x₃ + x₄ + x₅ = 20 , where
             x_i is the number distributed to location i .

      ii)   In how many of the distributions in (i) does location one receive at least 3 objects?

      iii)  In how many of the distributions in (i) does location one receive at most 3 objects?

      iv)  In how many of the distributions in (i) do locations one and two each receive at most 3 objects?