tag:blogger.com,1999:blog-2433841880619171855.post8297286252547792237..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Extending the Binomial DistributionUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2433841880619171855.post-52971985445574227142020-03-03T05:41:56.246+00:002020-03-03T05:41:56.246+00:00Data science is one of the top course in today'...Data science is one of the top course in today's career. Your content will going to helpful for all the beginners who are trying to find <a href="https://prwatech.in/blog/data-science/binomial-probability-distribution-tutorial/" rel="nofollow">Binomial Distribution Tutorial</a>. Thanks for sharing useful information. keep updating.Padminiprwatechhttps://www.blogger.com/profile/09684633881408922564noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-12271144689633092512010-12-23T01:06:33.111+00:002010-12-23T01:06:33.111+00:00A comment on JD2718's nice addition to my post...A comment on JD2718's nice addition to my post... Not only does " (a+b+c)^3 implies 3x3 multiplication, so 3 x 3 x 3 = 27 terms before combining like terms" because there are ten different terms after the like terms are combined, the sum of the coefficients of those ten terms must add up to .... 27. Now the student should figure what the sum of the exponents of (a+b+c)^4 would be, and how many terms there are,,,Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-52249886960123150362010-12-23T00:18:51.419+00:002010-12-23T00:18:51.419+00:00I love this stuff (and teach most of it in my &quo...I love this stuff (and teach most of it in my "combinatorics" elective).<br /><br />Look at this: (a+b+c)^3 implies 3x3 multiplication, so 3 x 3 x 3 = 27 terms before combining like terms:<br /><br />aaa / aab / aac<br />aba / abb / abc<br />aca / acb / acc<br />baa / bab / bac<br />bba / bbb / bbc<br />bca / bcb / bcc<br />caa / cab / cac<br />cba / cbb / cbc<br />cca / ccb / ccc<br /><br />But I like this piece better:<br />(a + b)^2 =<br />aa + ab + ba + bb<br />(what's the coefficient for ab? <==> how many ways can we rearrange ab)<br /><br />(a + b)^4 =<br />aaaa + aaab + aaba + aabb +<br />abaa + abab + abba + abbb + <br />baaa + baab + baba + babb +<br />bbaa + bbab + bbba + bbbb<br /><br />Coefficient for (a^2)(b^2)?<br />Same as the number of ways to rearrange aabb.<br /><br />This is fun.<br /><br />JonathanAnonymousnoreply@blogger.com