tag:blogger.com,1999:blog-7691251033406320222.post8442865562473633269..comments2024-03-26T04:19:38.862-07:00Comments on kitchen table math, the sequel: anonymous and Allison on choosing 2 out of 6 vs choosing 4 out of 6Catherine Johnsonhttp://www.blogger.com/profile/03347093496361370174noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-7691251033406320222.post-52289094563725042362011-04-26T12:16:08.794-07:002011-04-26T12:16:08.794-07:00an improved version of the last link.an <a href="http://vlorbik.wordpress.com/2011/04/26/for-catherine-j/" rel="nofollow">improved version</a> of the last link.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-35747439142998920122011-04-26T08:23:13.540-07:002011-04-26T08:23:13.540-07:00http://www.flickr.com/photos/36762583@N04/56580601...http://www.flickr.com/photos/36762583@N04/5658060190/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-45977519524817958442011-04-24T18:36:27.587-07:002011-04-24T18:36:27.587-07:00Glen - thank you!
Anonymous - I'm going to ha...Glen - thank you!<br /><br />Anonymous - I'm going to have to come back and read this tomorrow morning when I'm fresh!Catherine Johnsonhttps://www.blogger.com/profile/03347093496361370174noreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-82016422296947873722011-04-23T06:11:25.639-07:002011-04-23T06:11:25.639-07:00I'll try a shorter explanation.
Whether you c...I'll try a shorter explanation.<br /><br />Whether you choose 2 of 6 or 4 of 6, you do it by separating the 6 into two piles, one of 2 and one of 4. There are a certain number of ways you can do that. Whether you consider the 2-pile or the 4-pile the "chosen ones" doesn't change that number.Glennoreply@blogger.comtag:blogger.com,1999:blog-7691251033406320222.post-29564866504397282452011-04-22T19:41:46.054-07:002011-04-22T19:41:46.054-07:00I hope this explanation isn't overkill, so her...I hope this explanation isn't overkill, so here goes:<br /><br />Consider the following fun activity:<br />(1) Start with 6 balls, each engraved with a unique ID (like a social-security number).<br />(2) Get a supply of blank labels. Write "IN-THE-BOX" on 4 labels and "OUTSIDE-THE-BOX" on 2 labels.<br />(3) Place the 6 labels on the 6 balls any old way.<br /><br /><br />Now suppose that you and I both do this same fun activity. (We each use 6 balls with the same 6 IDs, etc.).<br />We both do the fun activity to see whether there's any difference in our results.<br /><br /><br />Question: Are there different (distinguishable) possible results from doing a fun activity repeatedly, i.e., more than one "way to label the balls"?<br />Answer: Yes. Suppose we both have a ball with ID 123-45-6789. Perhaps by chance you labelled yours IN-THE-BOX, but I labelled mine OUTSIDE-THE-BOX. This certifies that your result differs from mine.<br /><br />Question: So how many (distinguishable) results are possible when doing a fun activity?<br />Answer: 6C4.<br /><br />Question: If somebody does the fun activity as above, but instead writes "IN-THE-BOX" on 2 labels and "OUTSIDE-THE-BOX" on 4 lables, then how many results are there?<br />Answer: 6C2.<br /><br /><br />Now think about why these last two answers must be the same. If it helps, imagine writing LONDON on 4 labels and PARIS on 2 labels...<br />What's important is that some 4 labels are indistinguishable from one another, the other 2 labels are likewise indistinguishable from one another, but any one of the first 4 labels is distinguishable from any one of the other 2 labels.Anonymousnoreply@blogger.com