Comments on: Classroom violence, combinations, and permutations http://www.johndcook.com/blog/2009/09/02/selection-with-replacement/ The blog of John D. Cook Sat, 11 Feb 2012 01:10:06 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: CogitoErgoCogitoSum http://www.johndcook.com/blog/2009/09/02/selection-with-replacement/comment-page-1/#comment-36447 CogitoErgoCogitoSum Thu, 15 Apr 2010 21:51:21 +0000 http://www.johndcook.com/blog/?p=3024#comment-36447 I have a combinatorics question for you whose solution has thus far escaped me. There are 'n' objects. They are not necessarily unique. Unique element number one has a quantity of r₁, unique element number two has a quantity of r₂, so on so forth. In total, r₁ + r₂ + r₃ +... = n How many different <b>unique</b> permutations exist.... IF I take 'k' objects at a time? This was an attempt on my part to integrate problems involving permutation of n objects taken all n at a time with redundant elements, for which the solution is n!/(r₁! r₂! r₃!), and questions involving regular permutations without redundant elements taken k at a time, for which the solution is nPr. I have combined these two concepts into one question and Im stumped as to how to solve. I have a combinatorics question for you whose solution has thus far escaped me.

There are ‘n’ objects. They are not necessarily unique. Unique element number one has a quantity of r₁, unique element number two has a quantity of r₂, so on so forth. In total, r₁ + r₂ + r₃ +… = n

How many different unique permutations exist…. IF I take ‘k’ objects at a time?

This was an attempt on my part to integrate problems involving permutation of n objects taken all n at a time with redundant elements, for which the solution is n!/(r₁! r₂! r₃!), and questions involving regular permutations without redundant elements taken k at a time, for which the solution is nPr. I have combined these two concepts into one question and Im stumped as to how to solve.

]]> By: CogitoErgoCogitoSum http://www.johndcook.com/blog/2009/09/02/selection-with-replacement/comment-page-1/#comment-36446 CogitoErgoCogitoSum Thu, 15 Apr 2010 21:47:49 +0000 http://www.johndcook.com/blog/?p=3024#comment-36446 Is that the problem you gave in class? If so, I hope you at least taught how to solve it. Its not uncommon for teachers to do jack nothing all year long and expect the students to self-teach out of library books. It is your explicit job as a teacher to teach, not just tally grades and file them away with academia, as is oh so common among so-called "prestigious" schools. More like for-profit corporations who sell degrees, if you ask me. If you did teach this subject matter then your student should have known it. Im forced to ask how its possible the student could only assume it was one or the other if she had ever been taught a third or fourth way. Is that the problem you gave in class? If so, I hope you at least taught how to solve it. Its not uncommon for teachers to do jack nothing all year long and expect the students to self-teach out of library books. It is your explicit job as a teacher to teach, not just tally grades and file them away with academia, as is oh so common among so-called “prestigious” schools. More like for-profit corporations who sell degrees, if you ask me. If you did teach this subject matter then your student should have known it. Im forced to ask how its possible the student could only assume it was one or the other if she had ever been taught a third or fourth way.

]]> By: Carnival of Mathematics #57 « 360 http://www.johndcook.com/blog/2009/09/02/selection-with-replacement/comment-page-1/#comment-24377 Carnival of Mathematics #57 « 360 Sat, 12 Sep 2009 03:13:46 +0000 http://www.johndcook.com/blog/?p=3024#comment-24377 [...] over at The Endeavor,  a misunderstanding of those processes can (almost) lead to blows:  see Classroom Violence, Combinations, and Permutations for the full story. He also write about Gilbreath’s conjecture in Easy to Guess, Hard to [...] [...] over at The Endeavor,  a misunderstanding of those processes can (almost) lead to blows:  see Classroom Violence, Combinations, and Permutations for the full story. He also write about Gilbreath’s conjecture in Easy to Guess, Hard to [...]

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