Permutation

- It is an order arrangement of items whether the order must be strictly observed

Illustration

Assume x, y and z be any of three items. Arrange these in all possible permutations

NB: The above 6 permutations are the maximum one can ever acquire in a situation whereas there are only 3 items however if the number of items exceeds 3 then determining the number of permutations by outlining as done above may be cumbersome. Thus we use a special formula to find out such permutations. The formula is specified below

The number of permutations of 'r' items taken from a sample of 'n' items may be given as nPr =(n!)/((n - r)! )           

whereas; ! = factorial

For illustration

i. ³P₃ =(3!)/((3 - 3)! )

= (3 * 2 * 1) / )0!               Note that  0! = 1

6/1 = 1

ii. ⁵P₃ = (5!)/((5 - 3)! )     

 = (5 * 4 *3 * 2 * 1) / )1 * 2    

= 60

iii. ⁷P₅ =          (7!)/((7 - 5)! )

= (7 * 6 *5 * 4 *3 * 2 * 1) / )1 * 2

= 5040/2

= 2520