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May 16th, 2011, 04:28 PM  #1 
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Permutation and Combination
How many different way to arrange 12 stuffed animals on a counter ( 5 identical elephants and 7 identical monkeys )? How many different way to choose 5 from 12 monkey?? Why the answers of these question are same with one another !! I"M so confused 
May 16th, 2011, 04:58 PM  #2 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Permutation and Combination
Are we assuming that switching one monkey with another will still be the same combination?

May 16th, 2011, 05:08 PM  #3  
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Re: Permutation and Combination Quote:
 
May 16th, 2011, 05:12 PM  #4  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond  Re: Permutation and Combination Quote:
If a = b + c, a nCr b = a nCr c.  
May 16th, 2011, 05:19 PM  #5 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Permutation and Combination
In addition to to his explanation, there is a third way to find this. Take the total ways to arrange 12 stuffed animals, divide by the number of ways to arrange 7 monkeys, then divide again by the number of ways to arrange 5 elephants. This will eliminate combinations of monkeys and elephants that are switched with their own kind. This will also be the number of unique ways to arrange them.

May 16th, 2011, 08:59 PM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Permutation and Combination Hello, daivinhtran! Quote:
(a) Consider that there are 12 spaces on the counter. [color=beige]. . .[/color]Choose 5 spaces for the elephants.[color=beige] .[/color](The monkeys will go in the other 7 spaces.) [color=beige]. . .[/color] [color=beige]. . .[/color]Therefore, there are 792 ways to arrange the stuffed animals in a row. (b) There are 12 monkeys and we will choose 5 of them. [color=beige]. . .[/color] In both cases, we are choosing 5 objects from a set of 12 available objects.  
May 17th, 2011, 08:59 AM  #7  
Senior Member Joined: Mar 2011 Posts: 105 Thanks: 0  Re: Permutation and Combination Quote:
I got it, now, thank you  

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