Math 2602  A1-A3                                                                                 Homework  #5
                                          Due Thursday, September 29, 2005


     a)  How many of the words of length 20 which can be formed using the alphabet { A , C , G , T } have

          i)  exactly six A's ?

         ii)  exactly six A's and exactly 4 C's ?

   

     b)

          i) Find the number of ways to select, with replacement 15 objects from a set of five distince objects
              (when 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 = 15, 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 most 5 times.

          iii)  In how many of the selections in (i) is the first object obtained at least 3 times and the second
                object obtained at least 3 times?