The product rule
The product rule. Suppose that a procedure can be broken down into
two tasks T1 and T2. If there are n1 ways to do T1 and n2 ways to do T2
after that. Then there are n1n2 ways to do the procedure.
Generalization: If there are m tasks: T1,, T2 ,
, Tm that can be done
in n1, n2,
, nm ways, respectively, then there are n1n2
nm ways to
Example. How many different license plates are available if each
plate contains a sequence of three letters followed by a sequence of
--- 26 ? 26 ? 26 ? 10 ? 10 ? 10 =17,576,000
Example. How many possible grading results are there for the
midterm, if there are 16 students and the points they can get are
in the range from 0 to 100?