{"id":3748,"date":"2022-01-28T09:20:42","date_gmt":"2022-01-28T02:20:42","guid":{"rendered":"https:\/\/example.com\/?p=3748"},"modified":"2023-12-19T08:34:08","modified_gmt":"2023-12-19T01:34:08","slug":"kombinasi-dan-binomial-newton","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/kombinasi-dan-binomial-newton","title":{"rendered":"Kombinasi dan Binomial Newton dalam Aturan Pencacahan | Matematika Kelas 12"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-02.jpg\" alt=\"Kombinasi dan Binomial Newton dalam Aturan Pencacahan | Matematika Kelas 12\" width=\"820\" loading=\"lazy\" style=\"width: 820px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<blockquote>\n<p style=\"text-align: center;\"><em>Pada artikel matematika kelas 12 ini, kita akan membahas mengenai aturan pencacahan yakni kombinasi dan binomial Newton, Yuk kita belajar hari ini!<\/em><\/p>\n<p style=\"text-align: center;\">&#8212;<\/p>\n<\/blockquote>\n<p><!--more--><\/p>\n<p style=\"text-align: justify;\">Hi, <em>guys! <\/em>Kapan terakhir kali kamu belajar <a href=\"\/blog\/tag\/matematika-xii\" rel=\"noopener\" style=\"font-weight: bold;\">matematika<\/a>? Hayolo, kalau dah lama, mungkin sudah saatnya kita pengayaan materi lagi ya. Kali ini kita akan belajar tentang <strong>aturan pencacahan<\/strong>. Fokus pembahasannya pada <strong>kombinasi dan binomial Newton.<\/strong> Yuk, kita bahas satu-persatu ya.&nbsp;<span style=\"font-weight: 400;\"><\/span><\/p>\n<p style=\"font-size: 16px;\"><span style=\"font-weight: 400;\">&nbsp;<\/span><\/p>\n<h2 style=\"font-size: 20px;\"><span style=\"color: #000000;\"><strong style=\"background-color: transparent;\">Kombinasi<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">Kombinasi adalah <strong>banyak pilihan yang berbeda tanpa memperhatikan urutan ketika memilih r objek dari n objek<\/strong>.&nbsp; Kombinasi dinotasikan sebagai berikut:<\/span><\/p>\n<p><span style=\"font-weight: 400; color: #000000;\"><strong>Notasi kombinasi:&nbsp;<\/strong><\/span><\/p>\n<p><span style=\"font-weight: 400; color: #000000;\"><strong><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-03.jpg\" alt=\"Notasi kombinasi\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/strong><\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Untuk semua bilangan positif n dan r, dengan <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Capture-21.png\" alt=\"Capture-21.png\" width=\"113\" height=\"34\"><\/span><span style=\"font-weight: 400;\">, <\/span>banyaknya kombinasi r objek yang diambil dari n objek pada waktu yang sama, yaitu:<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-05.jpg\" alt=\"Rumus kombinasi\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<p style=\"text-align: center;\">&nbsp;<\/p>\n<h2 style=\"text-align: justify; font-size: 20px;\"><strong><span style=\"color: #434856;\">Contoh Soal Kombinasi<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\">1. Banyak cara memilih pemain inti untuk sebuah tim basket dari 9 orang adalah\u2026<\/p>\n<p style=\"text-align: justify; font-weight: bold;\">Jawab:<\/p>\n<p style=\"text-align: justify;\">Sebuah tim inti basket terdiri dari 5 orang, r = 5<\/p>\n<p style=\"text-align: justify;\">Banyak orang yang dapat dipilih, n = 9<\/p>\n<p style=\"text-align: justify;\">Banyak cara memilih 5 pemain inti tim basket dari 9 orang adalah:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-06.jpg\" alt=\"contoh soal kombinasi\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<p style=\"text-align: justify; font-weight: bold;\">Baca juga: <a href=\"\/blog\/pengenalan-istilah-statistik-data-tunggal-dalam-matematika\" rel=\"noopener\">Istilah Statistik Data Tunggal dalam Matematika<\/a><\/p>\n<p style=\"text-align: justify;\">&nbsp;<\/p>\n<p style=\"text-align: justify;\">2. Dari 4 penyanyi sopran dan 5 penyanyi alto akan dipilih empat orang pengurus paduan suara. Berapa banyak pilihan berbeda yang diperoleh jika dipilih 2 orang penyanyi sopran dan 2 orang penyanyi alto?<\/p>\n<p style=\"text-align: justify; font-weight: bold;\">Jawab:<\/p>\n<p style=\"text-align: justify;\">Banyak cara memilih 2 orang penyanyi sopran dari 4 penyanyi sopran, dan 2 penyanyi alto dari 5 penyanyi alto adalah:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-08.jpg\" alt=\"Contoh soal kombinasi\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<p>&nbsp;<\/p>\n<h2 style=\"font-size: 20px;\"><span style=\"color: #000000;\"><strong>Binomial Newton<\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\">Binomial newton adalah <strong>teorema yang menjelaskan mengenai penjabaran bentuk eksponensial aljabar dua suku.<\/strong> Dalam Binomial Newton menggunakan <strong>koefisien-koefisien (a + b)<sup>n<\/sup><\/strong>.<\/p>\n<p style=\"text-align: justify;\">Misalnya, n = 2 didapat: (a + b)<sup>2<\/sup> = (1) a<sup>2 <\/sup>+ 2ab + (1)b<sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\">Koefisien-koefisien hasil penjabaran (a + b)<sup>2<\/sup> adalah 1, 2, 1 yang senilai dengan C<sub>(2,0)<\/sub> dan C<sub>(2,2) <\/sub>dapat ditulis:<\/p>\n<p><span style=\"color: #000000;\"><em><span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Capture-24.png\" alt=\"Capture-24.png\" width=\"300\" height=\"43\"><\/span><\/span><\/em><\/span><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-04.jpg\" alt=\"Rumus Binomial Newton\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<p style=\"text-align: left; font-weight: bold;\">Baca juga: <a href=\"\/blog\/matematika-kelas-12-mengenal-ilmu-tertua-dalam-matematika-geometri\" rel=\"noopener\">Mengenal Ilmu Tertua dalam Matematika: Geometri!<\/a><\/p>\n<p style=\"text-align: left;\">&nbsp;<\/p>\n<h2 style=\"text-align: justify; font-size: 20px;\"><strong>Contoh Soal Binomial Newton<\/strong><\/h2>\n<p style=\"text-align: justify;\">1. Suku ketujuh dari penjabaran (2<em>x<\/em>+<em>y<\/em>)<sup>15<\/sup> adalah \u2026.&nbsp;<\/p>\n<p style=\"text-align: justify;\"><strong>Jawab:<\/strong><\/p>\n<p style=\"text-align: justify;\">dengan menggunakan rumus binomial newton,&nbsp;<\/p>\n<p style=\"text-align: justify;\"><em>n<\/em> =15<\/p>\n<p style=\"text-align: justify;\"><em>r <\/em>=7-1=6<\/p>\n<p style=\"text-align: justify;\">maka suku ketujuh dari penjabaran (2<em>x<\/em>+<em>y<\/em>)<sup>15<\/sup> adalah:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-07.jpg\" alt=\"Contoh soal binomial newton\" width=\"600\" loading=\"lazy\" style=\"width: 600px; margin-left: auto; margin-right: auto; display: block;\"><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\">Gimana, sudah mulai paham belum? Kalau kamu ingin dalami materi ini atau ingin belajar bab matematika yang lain, kamu bisa nih pelajari di konsep kilat <a href=\"https:\/\/ruangguru.com\/belajar?utm_medium=referral&amp;utm_source=blog&amp;utm_campaign=kombinasi-dan-binomial-newton-dalam-teori-peluang\" rel=\"noopener\" style=\"font-weight: bold;\" target=\"_blank\">ruangbelajar<\/a> pada bab<a href=\"\/blog\/mengetahui-percobaan-ruang-sampel-dan-menghitung-peluang-kejadian\" rel=\"noopener\"><strong> teori peluang, tentang percobaan, ruang sampel, dan peluang suatu kejadian<\/strong>.<\/a> Ada video animasi yang sangat menarik untuk bantuin kamu belajar. Tersedia juga rangkuman dan soal-soal latihan juga <em>lho<\/em>!<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/link.ruangguru.com\/blPk\/eaff0eb9\" target=\"_blank\" style=\"text-align: center;\" class=\"rg-cta\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/cta\/0ec4a2df-db2e-4ae1-8473-692756dcb684.jpeg\" width=\"822\" height=\"200\" alt=\"IDN CTA Blog ruangbelajar Ruangguru\" \/><\/a><\/p>\n<p><strong>Referensi:&nbsp;<\/strong><\/p>\n<p style=\"text-align: left;\">Sharma S. N, Widiastuti N, Himawan C, dkk (2017) Jelajah Matematika SMA Kelas XII Program Wajib. Jakarta:Yudisthira<\/p>\n<p>&nbsp;<\/p>\n<p><em>Artikel diperbarui 28 Januari 2022.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada artikel matematika kelas 12 ini, kita akan membahas mengenai aturan pencacahan yakni kombinasi dan binomial Newton, Yuk kita belajar hari ini! &#8212;<\/p>\n","protected":false},"author":49,"featured_media":3748,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Kombinasi%20dan%20Binomial%20Newton%20dalam%20Aturan%20Pencacahan%20-%20Matematika%20Kelas%2012-02.jpg"],"_edit_last":["1"],"_edit_lock":["1702949648:1"]},"categories":[467,476],"tags":[76,10,307,37],"class_list":["post-3748","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","category-matematika-sma-kelas-12","tag-kelas-12","tag-konsep-pelajaran","tag-matematika-xii","tag-sma"],"aioseo_notices":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Kombinasi dan Binomial Newton dalam Aturan Pencacahan | Matematika Kelas 12 - Belajar Gratis di Rumah Kapan Pun! 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