{"id":252,"date":"2022-04-12T06:38:32","date_gmt":"2022-04-12T06:38:32","guid":{"rendered":"http:\/\/5thclass.deltapublications.in\/?page_id=252"},"modified":"2025-02-07T05:40:09","modified_gmt":"2025-02-07T05:40:09","slug":"l-4-combinations","status":"publish","type":"page","link":"https:\/\/5thclass.deltapublications.in\/index.php\/l-4-combinations\/","title":{"rendered":"L.4 Combinations"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Combinations<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b;text-transform:capitalize\">Key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong>Definition of Combinations<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>A combination is a way of selecting items from a group where the order does not matter.<\/li>\n\n\n\n<li>Example: Choosing 2 fruits from {Apple, Banana, Orange} \u2192 {Apple, Banana}, {Apple, Orange}, {Banana, Orange}.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong>Difference Between Combinations and Permutations<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Combinations<\/strong>: Order does <strong>not<\/strong> matter. (Example: Choosing 2 team members from a group).<\/li>\n\n\n\n<li><strong>Permutations<\/strong>: Order <strong>does<\/strong> matter. (Example: Assigning 1st and 2nd place in a race).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong>Formula for Combinations<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>The formula for finding the number of ways to choose <strong>r<\/strong> items from <strong>n<\/strong> items is: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>C(n,r) = n! \/ r!(n\u2212r)!<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Example: Choosing 2 students from a group of 4 \u2192 <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>C(4,2) = 4! \/ 2!(4\u22122)! = 4\u00d73 \/ 2 \u00d7 1 = 6<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong>Examples of Combinations in Daily Life<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Choosing a group of friends for a trip.<\/li>\n\n\n\n<li>Selecting different toppings for a pizza.<\/li>\n\n\n\n<li>Forming teams in a class project.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong>Key Concept: Order Does Not Matter<\/strong><\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>If you select <strong>A and B<\/strong>, it is the same as selecting <strong>B and A<\/strong>.<\/li>\n\n\n\n<li>This makes combinations different from arrangements.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b1f8c0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-primary-color has-text-color\">\ud83c\udf00 Dwayne wants to get a sandwich from the deli for lunch. He can pick a roast beef, turkey, or tuna sandwich. The bread choices are white or multi-grain. <\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>How many different combinations can Dwayne pick from?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">\u200b&nbsp;_______ combinations<\/p>\n<\/div><\/div>\n\n\n\n<p>There are 3 sandwich choices and 2 bread choices. Multiply to find the number of possible combinations:<\/p>\n\n\n\n<p>3 \u00d7 2 = 6<br>There are 6 combinations.<\/p>\n\n\n\n<p>You could also make a list of all the combinations.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"263\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-3.png\" alt=\"\" class=\"wp-image-9366\" style=\"aspect-ratio:1.741444866920152;width:385px;height:auto\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-3.png 458w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-3-300x172.png 300w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure><\/div>\n\n\n<p>Now count the combinations. There are <strong>6<\/strong> combinations.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d1f9a8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-primary-color has-text-color\">\ud83c\udf00Riley is ordering a birthday cake for a friend. The bakery makes carrot, chocolate, and lemon flavoured cakes. Each flavour of cake can come with yellow or green frosting.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong> How many different combinations can Riley choose from?<\/strong><\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">\u200b&nbsp;________ combinations<\/p>\n<\/div><\/div>\n\n\n\n<p>There are 3 flavour choices and 2 frosting choices. Multiply to find the number of possible combinations:<\/p>\n\n\n\n<p>3 \u00d7 2 = 6<br>There are 6 combinations.<\/p>\n\n\n\n<p>You could also make a list of all the combinations.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"263\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4.png\" alt=\"\" class=\"wp-image-9369\" style=\"aspect-ratio:1.7300380228136882;width:460px;height:auto\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4.png 455w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-4-300x173.png 300w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/figure><\/div>\n\n\n<p>Now count the combinations. There are 6 combinations.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f7e4bc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-primary-color has-text-color\">\ud83c\udf00 Krysta is going out for a pasta dinner. She can choose fettuccine, shell, or macaroni pasta, and she can have garlic, cream, or pesto sauce. <\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">How many different combinations can Krysta have for dinner?<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">\u200b&nbsp;________ combinations<\/p>\n<\/div><\/div>\n\n\n\n<p>There are 3 pasta choices and 3 sauce choices. Multiply to find the number of possible combinations:<\/p>\n\n\n\n<p>3 \u00d7 3 = 9<br>There are 9 combinations.<\/p>\n\n\n\n<p>You could also make a list of all the combinations.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"366\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5.png\" alt=\"\" class=\"wp-image-9370\" style=\"aspect-ratio:1.2513661202185793;width:358px;height:auto\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5.png 458w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-5-300x240.png 300w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure><\/div>\n\n\n<p>Now count the combinations. There are <strong>9 <\/strong>combinations.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f <\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/83380\/336\/684\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-30.png\" alt=\"\" class=\"wp-image-5676\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-30.png 500w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-30-300x300.png 300w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-30-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84792\/388\/610\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-31.png\" alt=\"\" class=\"wp-image-5677\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-31.png 500w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-31-300x300.png 300w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-31-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Combinations Key notes : Definition of Combinations Difference Between Combinations and Permutations Formula for Combinations C(n,r) = n! \/ r!(n\u2212r)! C(4,2) = 4! \/ 2!(4\u22122)! = 4\u00d73 \/ 2 \u00d7 1 = 6 Examples of Combinations in Daily Life Key Concept: Order Does Not Matter Learn with an example \ud83c\udf00 Dwayne wants to get a<a class=\"more-link\" href=\"https:\/\/5thclass.deltapublications.in\/index.php\/l-4-combinations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;L.4 Combinations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-252","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/252","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=252"}],"version-history":[{"count":14,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/252\/revisions"}],"predecessor-version":[{"id":14645,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/252\/revisions\/14645"}],"wp:attachment":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}