Permutation Formula and Example

Permutation

Each different arrangement or ordered set of object is caused a permutation of those objects.

- if A = {a1, a2, a3……. An} is any set of n elements then any arrangement of the elements of “A” along a line is called a permutation of the elements of A.


All the permutation of the elements of the set is given by the formula:

P = n! where n = no. of elements

Problem:

How many permutations can be made from the word PINOY”

Solution:

PINOY – consist of 5 letters

P = 5! = 120 permutations

The total no. of permutations of n objects taken r at a time, P(n,r) is given by the expression.

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

Problem:

Find the no. of permutations of the four integers 1,2,3,4 taken two at a time.

Solution:

n = 4, r = 2

4P2 = n!/(n-r)! = 4!/(4-2)! = 4!/2! = 4.3.2.1 / 2.1 = 12