Permutations and Combinations
A selection of any r things out of n things in called a combination of n things taken r at a time. It is denoted by whereas a permutation is a set of unique objects that are arranged in a particular order, denoted by .
Let us see an example. Suppose you have to choose two out of three given fruits and order of choice does not matter.
Then your choices may be any one of the following:
These are the possible combinations of two fruits from a set of three fruits.
But, if you have to choose two out of three given fruits and order of choice matters. Then number of choices increase. Now your choices look like this:
Do you realize that earlier you had only three sets of two fruits each, but now you have six such sets.
Although the first set and the fourth have the same combination of fruits but the order of fruits are different in both.
Such cases where order is important are called permutations.
In this chapter you shall see how to arrive at the specific formulae for calculating the combinations and permutations of distinct as well as indistinct objects.