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Math A

 

A permutation  is an arrangement of objects in different orders. 
The order of the arrangement is important!!  For example, the number of different ways 3 students can enter school can be shown as  3!, or  3·2·1, or 6.  There are six different arrangements, or permutations, of the three students in which all three of them enter school.


     The notation for a permutation:       nPr
                                         n  is the total number of objects 
                                          r   is the number of objects chosen (want)

(Note  if  n = r   then   nPr  =  n!)

 

Examples:   1.    5P5 =     5·4·3·2·1  =  120


2.    6P2 =    6·5  =  30
               multiply two factors   (start with  6)

 

3.   7P5 =   7·6·5·4·3  =  2520
       The number of ways to arrange 5 objects that are
        chosen from a set of  7 different objects.

 

4.  What is the total number of possible 5-letter
       arrangements of the letters   w,h,i,t,e,  if each letter is
       used only once in each arrangement? 
          5P5   =   5·4·3·2·1   =   120
         ( 5 letters to choose from,  n#,  
            want 5-letter arrangements,  r#)

 

5.   How many different 3-digit numerals can be made from
       the digits of   45678   if a digit can appear just once in a
       numeral?
        5P3  =   5·4·3  =  60
      ( 5 numbers to choose from,  n#,
          want  3-digit numerals,  r#)       


                      


Schultzkie