Q&A #3398

Permutations and counting arrangements

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From: Claudia (for Teacher2Teacher Service)
Date: Apr 02, 2000 at 22:05:17
Subject: Re: Permutations and counting arrangements

I can't think of a "catchy" way, but basically, permutations deal with
arrangements.  I usually have my students draw little lines to represent how
many things I am arranging.  For example, if the problem says how many ways
can a family of five be seated in a row for a picture?  I have my students
make five blanks  ___ ___ ___ ___ ___
Then I go blank by blank and ask how many choices do I have...for the first
blank?  5
Second blank....since people can't be repeated there are 4 choices left
then 3
then 2
then 1
so the answer is 5 X 4 X 3 X 2 X 1 = 120 ways

Now suppose my mom and dad had to sit on the ends???
   ___  ___  ___  ___  ___

the first seat now only has 2 choices (mom or dad)
the second seat has only 3 choices (one of the kids)
work down...it looks like
    2  X  3  X  2  X  1  X  1  = 12 ways  (the last seat is a one because if
mom or dad sat in the first seat, it leaves only one person left)

Hope this helps

 -Claudia, for the Teacher2Teacher service

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