Math 2602  B1,B2                                                                         Homework  #5
                                          Due Tuesday, February 15, 2005


   i) Find the number of ways to select, with replacement , 12 objects from a set of five distinct objects
     (when the order in which they are selcted is not considered).

      Note:  This is the number of non-negative integer solutions to  x₁ + x₂ + x₃ + x₄ + x₅ = 12 , where
      x_i is the number of times object i is selected.

   ii) In how many of the selections in (i) is the first object obtained at least twice?

  iii) In how many of the selections in (i) is the first object obtained at most four times?

 iv)  In how many of the selections in (i) is neither the first nor second object obtained exactly 2 times?