{"id":89,"date":"2019-09-15T15:06:20","date_gmt":"2019-09-15T15:06:20","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=89"},"modified":"2019-09-15T15:06:20","modified_gmt":"2019-09-15T15:06:20","slug":"aops-cp_1-counting-is-arithmetic","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2019\/09\/15\/aops-cp_1-counting-is-arithmetic\/","title":{"rendered":"AOPS CP_1. Counting is Arithmetic"},"content":{"rendered":"<p><strong>Lesson Review:<\/strong><\/p>\n<p>1. The number of items in the list: a, a+1, &#8230;, b, b-1, where a\u2264b are integers, is b-a+1 (understand how it is derived).<\/p>\n<p>2. Understand <strong>Venn Diagram<\/strong><\/p>\n<p><a href=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/09\/VDIntersections.png\"><img loading=\"lazy\" class=\"alignnone size-medium wp-image-90\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/09\/VDIntersections-300x291.png\" alt=\"VDIntersections\" width=\"300\" height=\"291\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/09\/VDIntersections-300x291.png 300w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/09\/VDIntersections-1024x994.png 1024w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/09\/VDIntersections.png 1362w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>3. Count multiple events: (the number of ways A can occur) times (the number of ways B can occur)<\/p>\n<p>4. <strong>Permutation<\/strong>: selelct r items in order from a group of n items in P(n,r) ways:<\/p>\n<p>P(n,r) =\u00a0n x (n-1) x (n-2) x &#8230; (n-r+2) x (n-r+1) = n!\/(n-r)!<\/p>\n<p>5. <strong>Factoral<\/strong>: n! = n x (n-1) x (n-2) x &#8230; 3 x 2 x 1<\/p>\n<p><strong>Homework:<\/strong><\/p>\n<p>Page 5: Ex 1.2.1, 1.2.2, 1.2.6<\/p>\n<p>Page 12: Ex 1.3.1, 1.3.3<\/p>\n<p>Page 18: Ex 1.4.1, 1.4.3, 1.4.5<\/p>\n<p>Page 21: Ex. 1.5.1 (a) (c), 1.5.2<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lesson Review: 1. The number of items in the list: a, a+1, &#8230;, b, b-1, where a\u2264b are integers, is b-a+1 (understand how it is derived). 2. Understand Venn Diagram 3. Count multiple events: (the number of ways A can occur) times (the number of ways B can occur) 4. Permutation: selelct r items in [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/89"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=89"}],"version-history":[{"count":1,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/89\/revisions"}],"predecessor-version":[{"id":91,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/89\/revisions\/91"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=89"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=89"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=89"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}