{"id":1858,"date":"2022-08-30T06:29:00","date_gmt":"2022-08-29T23:29:00","guid":{"rendered":"https:\/\/example.com\/?p=1858"},"modified":"2023-12-19T08:33:55","modified_gmt":"2023-12-19T01:33:55","slug":"jenis-permutasi-dalam-teori-peluang","status":"publish","type":"post","link":"https:\/\/staging-blog.sirogu.com\/blog\/jenis-permutasi-dalam-teori-peluang","title":{"rendered":"Yuk, Belajar 5 Jenis Permutasi dalam Teori Peluang | Matematika Kelas 12"},"content":{"rendered":"

\"Matematika
<\/span><\/p>\n

\n

Yuk, sama-sama kita belajar jenis-jenis permutasi dalam teori peluang! Ada apa saja, ya?<\/em><\/p>\n<\/blockquote>\n

—<\/span><\/p>\n

<\/span><\/p>\n

Setelah kamu belajar tentang aturan perkalian dan faktorial<\/strong> dalam teori peluang, sekarang kita akan lanjut belajar mengenai permutasi. Apa itu permutasi? Nah, permutasi adalah susunan unsur berbeda yang dibentuk dari n unsur, diambil dari n unsur atau sebagian unsur. Permutasi dapat dikelompokkan menjadi beberapa macam. Dalam artikel ini, kita akan belajar tentang jenis permutasi dalam teori peluang. Kira-kira apa saja ya jenis-jenis permutasi itu? Yuk<\/em>, simak artikel berikut!<\/span><\/span><\/span><\/p>\n

\"Rumus<\/span><\/span><\/p>\n

Rumus-rumus permutasi dalam teori peluang<\/em><\/p>\n

 <\/p>\n

1. Permutasi dari n elemen, tiap permutasi terdiri dari n elemen<\/h2>\n

Jika ada unsur yang berbeda, diambil n unsur, maka banyaknya susunan (permutasi) yang berbeda dari n unsur tersebut adalah: <\/span><\/p>\n

\"rumus<\/span><\/p>\n

Contoh:<\/strong><\/p>\n

Untuk menyambut sebuah pertemuan delegasi negara yang dihadiri oleh lima negara, panitia akan memasang kelima bendera dari lima negara yang hadir. Banyak cara panitia menyusun kelima bendera tersebut adalah \u2026<\/span><\/p>\n

Jawab:<\/p>\n

Dari lima bendera yang ada, berarti n = 5, maka banyak susunan bendera yang mungkin yaitu:<\/span><\/p>\n

5! = 5.4.3.2.1 = 120 cara.<\/span><\/p>\n

Baca juga: Rumus Bunga Majemuk dan Cara Menghitungnya<\/a><\/p>\n

 <\/p>\n

2. Permutasi n elemen, tiap permutasi terdiri dari r unsur dari n elemen dengan r \u2264 n<\/h2>\n

Untuk semua bilangan positif n dan r, dengan <\/span>r \u2264 n<\/span>, banyaknya permutasi dari n objek yang diambil r objek pada satu waktu adalah:<\/span><\/p>\n

\"rumus
<\/span><\/p>\n

rumus permutasi ini memiliki syarat, yaitu urutan harus diperhatikan, ya!<\/span><\/em><\/p>\n

 <\/p>\n

Contoh:<\/strong><\/p>\n

Banyak cara untuk memilih seorang ketua, sekertaris dan bendahara dari 8 siswa yang tersedia adalah\u2026<\/span><\/p>\n

Jawab:<\/p>\n

Banyak siswa, n = 8<\/span><\/p>\n

Ketua, sekretaris dan bendahara (banyak pilihan objek), r = 3<\/span><\/p>\n

Maka:<\/span><\/p>\n

\"latihan<\/span><\/p>\n

 <\/p>\n

3. Permutasi dari n unsur yang mengandung p.q dan r unsur yang sama<\/h2>\n

 <\/p>\n

\"rumus
<\/strong><\/span><\/p>\n

Keterangan: <\/span><\/p>\n

n    = banyaknya elemen seluruhnya<\/span><\/p>\n

k<\/span>1 <\/span><\/sub> = banyaknya elemen kelompok 1 yang sama<\/span><\/p>\n

k<\/span>2<\/span><\/sub>  = banyaknya elemen kelompok 2 yang sama<\/span><\/p>\n

\u2026<\/span><\/p>\n

k<\/span>t<\/span><\/sub>   = banyaknya elemen kelompok kt yang sama<\/span><\/p>\n

t = 1,2,3,\u2026<\/span><\/p>\n

 <\/strong><\/span><\/p>\n

Contoh:<\/strong><\/p>\n

Banyak cara untuk menyusun dari kata \u201dBASSABASSI\u201d adalah\u2026<\/span><\/p>\n

Jawab:<\/p>\n

Dari kata \u201dBASSABASSI\u201d, banyak huruf (n) = 10<\/span><\/p>\n

k<\/span>1 <\/span><\/sub>= huruf B = 2<\/span><\/p>\n

k2<\/sub> = huruf A = 3<\/span><\/p>\n

k3<\/sub> = huruf S = 4<\/span><\/p>\n

k4<\/sub> = huruf I = 1<\/span><\/p>\n

\"latihan<\/span><\/p>\n

Baca juga: Istilah-Istilah Data Tunggal dalam Matematika<\/a><\/p>\n

 <\/p>\n

4. Permutasi Siklis<\/h2>\n

Permutasi siklis adalah permutasi melingkar (urutan melingkar).<\/span><\/p>\n

\"rumus<\/p>\n

Contoh:<\/strong><\/p>\n

Dari 5 orang anggota keluarga akan duduk mengelilingi sebuah meja bundar, banyak cara susunan yang dapat dibuat dari 5 orang tersebut adalah…<\/span><\/p>\n

Jawab:<\/p>\n

Banyak orang (n) = 5, maka :<\/span><\/p>\n

5<\/span><\/sub>P<\/span>siklis<\/span><\/sub> = (5 \u2013 1)! = 4! = 4.3.2.1 = 24 cara.<\/span><\/span><\/p>\n

 <\/p>\n

5. Permutasi berulang dari n unsur, tipe permutasi terdiri dari k unsur<\/h2>\n

 <\/strong><\/span><\/span><\/p>\n

\"rumus<\/strong><\/span><\/span><\/p>\n

Contoh:<\/strong><\/p>\n

Banyak susunan 3 bilangan dari angka-angka 1, 2, 3, 4, 5 dan 6 adalah\u2026<\/span><\/p>\n

Jawab:<\/p>\n

Banyak susunan 3 bilangan, berarti bilangan ratusan, k = 3<\/span>
<\/span>Banyak angka yang akan disusun, n = 6<\/span>
<\/span>Banyak susunan 3 bilangan dari angka 1, 2, 3, 4, 5, dan 6:<\/span><\/p>\n

P<\/span>6<\/span><\/sub> = 6<\/span>3<\/span><\/sup> = 216 susunan.<\/span><\/p>\n

 <\/p>\n

Oke, setelah kamu memahami perbedaan dari 5 jenis permutasi dan contoh soalnya, sekarang, coba kamu kerjakan beberapa latihan soal permutasi berikut ini, yuk!<\/span><\/p>\n

 <\/p>\n

Latihan Soal Permutasi<\/h2>\n

1. Ada berapa cara bila 4 orang siswa (misal: a, b, c, d) menempati tempat duduk yang akan disusun dalam suatu susunan yang teratur?<\/p>\n

2. Suatu kelompok ekskul tari yang terdiri dari 3 siswa laki-laki dan 5 siswa perempuan akan memilih 3 orang pengurus. Berapa cara yang dapat dibentuk dari pemilihan jika pengurus terdiri dari 2 siswa laki-laki dan 1 siswa perempuan.<\/p>\n

3. Dalam sebuah kantong terdapat 7 kelereng. Berapa banyak cara mengambil 4 kelereng dari kantong tersebut?<\/p>\n

—<\/span><\/p>\n

Sekarang sudah mengerti <\/span>kan<\/span><\/i> tentang jenis permutasi? Pada artikel selanjutnya, kamu bisa melanjutkan belajar tentang teori peluang yang fokus pada pembahasan <\/span>kombinasi dan binomial newton<\/strong><\/a>. <\/strong><\/p>\n

Masih bingung tentang permutasi? Yuk<\/em> belajar bersama dengan video animasi yang keren hanya di ruangbelajar<\/strong><\/a>!<\/p>\n

\"IDN<\/a><\/p>\n

Sumber Referensi: <\/strong><\/p>\n

Sharma S. N, Widiastuti N, Himawan C, dkk (2017) Jelajah Matematika SMA Kelas XII Program Wajib. Jakarta:Yudisthira<\/p>\n

 <\/p>\n

Artikel diperbarui 30 Agustus 2022.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Yuk, sama-sama kita belajar jenis-jenis permutasi dalam teori peluang! Ada apa saja, ya? —<\/p>\n","protected":false},"author":16,"featured_media":1858,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_knawatfibu_url":["https:\/\/cdn-web.ruangguru.com\/landing-pages\/assets\/hs\/Matematika%2012%20-%20Jenis%20Peluang-02.jpg"],"_edit_last":["1"],"_edit_lock":["1702949635:1"]},"categories":[467,476],"tags":[76,10,307,37],"class_list":["post-1858","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":"\nYuk, Belajar 5 Jenis Permutasi dalam Teori Peluang | Matematika Kelas 12 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/staging-blog.sirogu.com\/blog\/jenis-permutasi-dalam-teori-peluang\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Yuk, Belajar 5 Jenis Permutasi dalam Teori Peluang | Matematika Kelas 12 - Belajar Gratis di Rumah Kapan Pun! | Blog Ruangguru\" \/>\n<meta property=\"og:description\" content=\"Yuk, sama-sama kita belajar jenis-jenis permutasi dalam teori peluang! 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