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. ^{3}P_{3 }=(3!)/((3 - 3)! )
= (3 * 2 * 1) / )0! Note that 0! = 1
6/1 = 1
ii. ^{5}P_{3 }= (5!)/((5 - 3)! )
= (5 * 4 *3 * 2 * 1) / )1 * 2
= 60
iii. ^{7}P_{5} = (7!)/((7 - 5)! )
= (7 * 6 *5 * 4 *3 * 2 * 1) / )1 * 2
= 5040/2
= 2520