# Aptitude Permutation and Combination

## Permutation

In mathematics, permutation is the different arrangement of a given number of things by taking some or all at a time.

## Combination

The **combination** is a way of selecting items from a collection, such that the order of selection does not matter.

## Important formula

Let n be a positive integer. Then, factorial n, denoted n! is defined as:

n! = n(n - 1)(n - 2) ... 3.2.1.

#### Examples:

- We define 0! = 1.
- 3! = ( 3 x 2 x 1) = 6.
- 4! = (4 x 3 x 2 x 1) = 24.

### Number of Permutations:

Number of all permutations of n things, taken r at a time, is given by:

### Examples:

^{5}P_{2} = (5 x 4) = 20.
^{4}P_{3 }= (4 x 3 x 2) = 24.

#### Important result

If there are n subjects of which p_{1} are alike of one kind; p_{2} are alike of another kind; p_{3} are alike of third kind and so on and pr are alike of rth kind,
such that (p_{1} + p_{2} + ... p_{r}) = n.

Then, number of permutations of these n objects is =