Permutation

Permutation

Permutation is simply the different ways you can arrange things where the order matters.

Permutation has to do with each of the various ways a set of objects can be arranged.

It means how you line things up is very important.

It is the changing of the arrangement of several items, with respect to the order of arrangement.

This means that if you have three students named Ade, Bola, and Chinwe, the arrangement ABC is not the same thing as ACB because the positions have changed.

What this implies is that ABC is different from ACB. In other words, permutation means choosing r items from a set of n objects.

Permutation Formula

We use a special sign to show permutation, which is written as nPr.

Permutation is denoted with ( nPr ).

If you are arranging things and you are not allowed to use one item more than once, use this formula below.

The formula for permutation without repetition is given as

nPr = P ( n, r ) = n! / ( n - r )!

If you are allowed to use the same item many times, the formula changes.

When repetition is allowed, the formula is given as

nPr = n^r

Where

n is the total number of items you have to pick from.

r is how many items you are picking at a time.

! is called the factorial symbol.

What is Factorial

Factorial is a way to find how many ways you can arrange a specific number of things.

Evaluating the factorial of a number implies "in how many ways can the number be arranged?".

To solve it, just multiply that number by every whole number smaller than it until you reach one.

The way to go about this is to represent the number as 'n' and apply this formula.

(n) x (n - 1) x (n - 2) x ... 1

Note that you continue like that until you get to ... x 1.

Examples of Factorial

2! = (2) x (2 - 1) = 2 x 1 = 2

3! = (3) x (3 - 1) x (3 - 2) = 3 x 2 x 1 = 6

4! = (4) x (4 - 1) x (4 - 2) x (4 - 3) = 4 x 3 x 2 x 1 = 24

5! = (5) x (5 - 1) x (5 - 2) x (5 - 3) x (5 - 4) = 5 x 4 x 3 x 2 x 1 = 120