Math 2602 A1 - A3                                                                                    Homework #5
                                              Due Tuesday , February 10 , 2004

1.  How many binary strings of length 16 have

   i)  exactly 5 ones?

  ii) exactly 5 ones in the leftmost 8 positions and exactly 5 ones in the rightmost 8 positions?


2.  Find the number of ways to select 10 objects with repetition from a set of 4 (distinct)
     objects (if the order in which they are selected is not considered) and

   i) the first object is obtained at least 4 times.

  ii) the first object is obtained at most 3 times.

 iii) each of the first two objects is obtained at most 3 times.