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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: 2000062116:49:03
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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