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Counting principle:
If the set E contains n elements and the set F contains m elements, there are 
ways in which we can choose first an element of E and then element
of F.
Example:
We toss a coin two times. This experiment has two steps: the first step toss, the second toss. Each step has two outcomes: a head and a tail. Thus, total outcomes for two tosses of a coin= 
.
The four outcomes for this experiment are: HH, HT, TH, TT
Generalized counting principle:
Let 
be sets with 
elements, respectively. Then there are 
ways in which we can first choose an element of 
, then an element of 
,……., and finally an element of 
.
Example:
How many outcomes does the experiment of throwing five dice have?
Solution:
Let 
, 
be set of all possible outcomes of 
die. Then 
. The number of the outcomes of the experiment of throwing five dice equals the number of ways we can first choose an element of , then an element of ,….., and finally an element of 
.
That is 
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