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Combination
A combination is a selection of all or part of a
set
of objects, without regard to the order in which objects are
selected.
For example, suppose we have a set of three letters: A, B, and C. We might ask
how many ways we can select 2 letters from that set. Each possible selection
would be an example of a combination. The complete list of possible selections
would be: AB, AC, and BA.
Computing the number of combinations. The
number of Combinations of
n objects taken
r at a time is
nCr = n(n - 1)(n
- 2) ... (n - r + 1)/r! = n! / r!(n - r)! = nPr / r!
Note that AB and BA are considered to be one combination, because the order in
which objects are selected does not matter. This is the key distinction between
a combination and a permutation.
A combination focuses on the selection of objects without regard to the
order in which they are selected. A permutation, in contrast, focuses on the
arrangement of objects with regard to the order in which they are
arranged.