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Q&A #3398

Teachers' Lounge Discussion: Permutations and counting arrangements

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From: Jeanne 
To: Teacher2Teacher Public Discussion
Date: 2000062115:49:03
Subject: Re: Permutations

I like to put things in a context when I can.

For example, I might ask my students:  "How many different ways can 8
students stand in single file for recess?"

   ___  ___  ___  ___  ___  ___  ___  ___
   1st  2nd  3rd  4th  5th  6th  7th  8th

Ask your student, "From your group of 8 students, how many COULD be
1st?"
Answer:  8

   _8_  ___  ___  ___  ___  ___  ___  ___
   1st  2nd  3rd  4th  5th  6th  7th  8th

"How many choices do we have for 2nd?"  The two most common answers
are 8 and 7.  The correct answer is 7.  To get the kids to see that 7
is correct I like to have them act out the problem, use
pictures/diagrams, or manipulatives.  Once the 1st place person is
"chosen", there are only 7 remaining students from whom to choose for
2nd.

   _8_  _7_  ___  ___  ___  ___  ___  ___
   1st  2nd  3rd  4th  5th  6th  7th  8th

"How many choices do we have for 3rd?"  Answer: 6

   _8_  _7_  _6_  ___  ___  ___  ___  ___
   1st  2nd  3rd  4th  5th  6th  7th  8th

It usually doesn't take too long for the kids to get the rest of the
places.

   _8_  _7_  _6_  _5_  _4_  _3_  _2_  _1_
   1st  2nd  3rd  4th  5th  6th  7th  8th

We have 8*7*6*5*4*3*2*1 or 8 factorial or 8!


Hope this helps.

 -Jeanne, for the Teacher2Teacher service


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