Combinations

The word combination means selection. Suppose you are asked to make a selection of any two things from three things: a, b and c.

The different selections are: ab, bc, ac

Here, there is no reference to the order in which they are selected, ab and ba denote the same selection. These selections are called combinations.

A selection of any r things out of n things is called a combination of n things r at a time. It is denoted by ⁿC_r.

In a combination only selection is made whereas in a permutation not only a selection is made but also an arrangement in a definite order is considered.
In a combination, the ordering of the selected objects is immaterial whereas in a permutation, the ordering is essential.
Usually the number of permutation exceeds the number of combinations.
Each combination corresponds to many permutations.

The number of all combinations of n distinct objects, taken r at a time is given by