1).  a) 10    b) 15    c) 21    d) 28

         2).  a) 5     b) 15    c) 35    d) 70 

         3)   a) 4     b) 8     c) 16    d) 31     e) 57

    Notes

  1). The number of lines equals the number of pairs of
       points, or nC2, or n(n-1)/2.

  2). The number of intersections equals the number of
       quadruplets of points, or nC4, or
       n(n-1)(n-2)(n-3)/24.

  3). If the lines are drawn one at a time, a new area is
       formed whenever (i) an intersection occurs or (ii) a  
       line is completed. Initially there is one area, so
       total is 1 + nC2 + nC4.

  In an election there were only three parties. The Constrictive
   Party gained c% of the votes, The Grey Party gained g% and
   the Socratic Party gained s%, so that c + g + s = 100 (for
   example c = 37.61, g = 18.23, s = 44.16.). But before publication
   the three percentages were rounded to the nearest whole number,
   giving C%, G% and S% respectively (in the example 38, 18, 44).
  
  1. Find the probability that c differs from C by more than 0.25.

  2. Find the probability that when the combined percentage vote for 
      the Constrictive and Grey Parties is itself rounded to the
      nearest whole number, the result is not equal to C + G.

  3. Find the probability that C + G + S = 101.