PERMUTASI

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PERMUTASI adalah suatu pengacakan dengan memperhatikan urutan.

Contoh ::

H={a1 , a2 , a3} , di dalam pengacakan 2 dari himpunan H, H1={(a1 , 12), (a1 , a3), (a2 , a1), (a2 , a3), (a3 , a1), (a3 , a2)} dimana (a1 , 12) ≠ (a1 , a3)≠ (a2 , a1)≠ (a2 , a3)≠ (a3 , a1)≠ (a3 , a2)

n(H1)= 6 anggota

H1 dilambangkan sebagai P(2,H)

n(H1) = n(P(2,H)) = 6

P(3,H) = {(a1 , a2 , a3), (a1 , a3 , a2), (a2 , a1 , a3), (a2 , a3 , a1), (a3 , a1 , a2), (a3 , a2 , a1)}

n(H) = 3 → P(3,3) = 6

Misal ada H2={(a1 , a2)}

P(2,H2) = {(a1 , a2), (a2 , a1)} → P(2,2) = 2

Misal ada H3={a1}

P(1,H3) = {(a1)} → P(1,1) = 1

Catatan :

Permutasi merupakan prinsip di perkalian..

P(1,1) = 1

P(2,2) = 2 = 2 x 1

P(3,3) = 6 = 3 x 2 x 1

P(n,n) = n(n-1)(n-2)(n-3)….. 3 . 2 . 1

P(n,n) = n!

Bagaimanakah untuk P(r,n)???

dengan prinsip perkalian, terdapat r kejadian berbeda

n1 → n

n2 → (n-1)

n3 → (n-2)

.

.

nr → (n-(r-1)) = (n-r+1)

dengan prinsip perkalian ::

P(r,n) = n1, n2, n3, n4,….,nr

P(r,n)=n(n-1)(n-2)(n-3)……(n-r+1)

sehingga :

P(r,n)= n(n-1)(n-2)(n-3)……(n-r+1)(n-r)! / (n-r)!

P(r,n)= n/(n-r)!

About NICO MATEMATIKA

Welcome to my blog. My name is Nico. Admin of this blog. I am a student majoring in mathematics who dreams of becoming a professor of mathematics. I live in Kwadungan, Ngawi, East Java. Hopefully in all the posts I can make a good learning material to the intellectual life of the nation. After the read, leave a comment. I always accept criticism suggestion to build a better me again .. Thanks for visiting .. : mrgreen:

Posted on June 14, 2011, in education and tagged , . Bookmark the permalink. 17 Comments.

  1. Pusing mirin rumus..hehe

  2. hahaha.
    ini di-posting untuk menjawab pertanyaanku yak? *geer* *pedee* *ngakak*
    *gulingguling* *kebanyakan*
    haha. berarti besok kombinasinya! *ngakak lagi*

  3. Wah anak sy bisa kursus disini. Terus posting mas!

  4. Kaya pernah kenal nih sama mutasi-mutasi ini.
    Sayang bukan anak matematika, yang saya kenal cuma mutasi genetik. hehehe

  5. Ampun, pusing saya bacanya😆

  6. pusssiinggg…
    izin singgah…(punten, nyasar disini…)
    salam kenal

  1. Pingback: daftar isi « matematika blog for education

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