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 =