Math 2602 A1 , A2 , A3                                                                   Homework  # 5

                                                     Due Tuesday, February 11, 2003

   i)  Find the number of ways to distribute  20 indistinguishable objects to 4 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 = 20 , where
       x_i is the number distributed to location i , for i = 1, 2, 3, 4 .


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


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


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