1).  6

  2).  13

  3).  8

     Notes

      1). Suppose x electors voted for A & B
                  y electors voted for     B & C
                  z electors voted for A     & C

               Then  x     + z = 10
                     x + y     = 9
                         y + z = 7

               Solving, x = 6
                        y = 3
                        z = 4

      Questions 2) and 3) may be solved by similar methods.

  1. The streets of the town of Yuletideville all run either
      North-South or East-West, as shown. Each day a certain
      Mr. Noel Carol who lives near junction A walks to his
      office near junction B. How many different routes can
      he take, assuming he walks no unnecessary distance?

  2. If his office is moved to a new location at C, how many
      routes can he then take for his walk to work?

  3. If the office has yet another move to D, how many routes
      can he then take?