We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. The minimum number of voters required to form a manipulating coalition can be expressed as the solution of an integer linear program. In the limiting case of a large electorate, the problem simplifies enough that a central limit theorem can be derived. It is seen that the manipulation resistance of positional rules with 5 or 6 (or more) candidates is quite different from the more commonly analyzed 3- and 4-candidate cases.