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Math A

 

In general, repetitions are taken care of by dividing the permutation by the number of objects that are identical! (factorial)

Example:

                 1.  How many different 5-letter words can be
                     formed from the word   APPLE  ?

     =    5·4·3·2·1      =   120    =    60 words
               2·1                   2

                           You divide by  2! because the letter  P repeats twice.

                  

                      2.  How many different six-digit numerals can be
                     written using all of the following six digits:
                     
4,4,5,5,5
,7

    =    6·5 ·4·3·2·1     =    720   =   60
          2·1  ·   3·2·1           12

                          Two fours repeat and three fives repeat.
                         
         2!                               3!

                      


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