Some basic counting laws include: . Complement law: If an event can have n different possible outcomes, and a particular event can occur in k different ways, then the number of ways the particular event cannot occur is n - k. . Addition law: If n mutually exclusive events can occur in 1, k2, . .., kn different ways, then the number of ways any one of the events can occur is k1 + k2 + . . . + kn. . Multiplication law: If n independent events can occur in k1, k2, . .., kn different ways, then the number of ways every event can occur together is kik2 . . . kn. A string of digits is any sequence of digits (0,1,2,3,4,5,6,7,8,9) in order. A string may start with 0, so valid 7-digit strings include 3822706 and 0240636