Combinations: Order Doesn't Matter
Examples: Out of the set S = {A, B, C}
, a combination set would include AAA
, AAB
, ABC
, .... etc, and ABA = BAA
because order doesn't matter. When order doesn't matter, you don't need to count as many things, e.g. if AAB
is equivalent to ABA
, then those items count as one element of the set, not two.
Permutations: Order Matters
Note that the denominator is smaller than in combinations. Permuations possibilities are much larger because order matters, so we have to count it all.
Examples: Out of the set S= {A, B, C}
, a combination set would include AAA
, AAB
, ABC
, .... etc, and ABA != BAA.
Cardinality is the number of elements in a Set.
Probability is the likelihood that an event will occur.
Events The probability of an event
E
is the cardinality of the event|E|
divided by the cardinality of the sample space|S|
(the "universe",S
,) that the event is in.
To be continued ...