Permutation Formula

Permutations: An arrangement of things where the order is important

Formula: nPr=       n!              n= total # of objects   n≥r
                         (n-r)!           r= # of objects selected out of n 

The factorial (!) sign means to multiply all of the positive integers from n consecutively down to 1.
You can use this formula only when there are no repetitions and restrictions. 
Assume no repetitions are allowed unless otherwise.
Repetition means you are allowed to pick the same item more than once and Restrictions are when you are asked to place an item in a specific location.
Note: nP1=n! |  nP0= 1 | nPn=n! (0!=1)

For example:
How many three letter words composed from the 26 letters in the alphabet are possible? (assume no repetitions)
n=26 r=3
nPr=     n!      =         26!      =      26!      =      26*25*24*23!    
         (n-r)!            (26-3)!           23!                   23!

= 26*25*24= 15600

Repetitions allowed  
You cant use the formula but you can use the dash method 

    26          *         26          *    26           = 17576 
1st Letter         2nd Letter      3rd Letter
can be any       can be any      can be any

Restrictions 
How many 4 letter "words" beginning with A are possible, given the word MAPLES

  1    *     5        *       4        *        3     =  160
Must    5 letters      4 letters       3 letters
Be A     to chose      to chose        to chose
              from           from              from 

Example 2: Evaluate 
7P3
n=7        7P3=     7!       =  7!   =   7*6*5*4!   = 7*6*5 = 210
r=3                   (7-3)!        4!              4! 

Exmaple 3: solve
nP1=20                                                                          
n=n! r=1      
             nP1=20
             n!     = 20
           (n-1)!
            n(n-1)!  = 20
            (n-1)!

              n=20