A permutation is an ordered arrangement of objects.

Ex. If you have n objects to choose from you have n options for the first object, (n-1) options for teh second, (n-2) for the third and so on.

Therefore the number of different permutations for n objects is

n! = n(n-1)(n-2)(n-3)…….1

This is called the factorial of n!

If you wish to select r objects out of n objects this can be done in

n (n-1) (n-2)……(n-r+1) = n!/(n-r)! = P(n, r)  different ways.

Ex. The number of permutations of the 8 letters in the word SCARLET is:

8! =8* 7*6*5*4*3*2*1 = 40 320.

If oe is content with four of the letters the number of possibilities is

8!/(8-4)! = 8!/4!=1680 .

If redundance is forbidden the number of possibilitites decreases by one for every further step of the selection. The total number of possibilities for selction of r objects out of n then becomes (according to the multiplication principle)

n(n-1)(n-2) …. (n-r+1).