What is Permutations explain with examples?

Each arrangement of a set of elements is called a permutation. In other words, every possible way (order) of writing a group of letters, numbers, etc., is called a permutation of that set.

For example, how many ways can Ada, Brenda, and Chad sit in a row ("a" represents Ada, "b," Brenda, and "c," Chad).

There are 6 permutations in which to arrange a, b, c. Therefore, there are 6 ways Ada, Brenda, and Chad can sit in a row.

Factorial

A factorial is a number with a factorial sign ("!") after it.

5! is read "five factorial."

3! is read "three factorial."

See if you can figure out what the factorial sign does to the numbers below:

5! = 5 x 4 x 3 x 2 x 1

3! = 3 x 2 x 1

The factorial of a number is the product of that number and all the whole numbers less than it, stopping at 1.

Use factorials in finding the number of permutations. The number of permutations equals the factorial of the number of objects.

For example, the number of different orders in which you can arrange 4 video tapes on a shelf is 4!

4! = 4 x 3 x 2 x 1 = 24

There are 24 ways to arrange 4 video tapes on a shelf.